policy_gradient_method/actor_critic.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "9a8b6024",
   "metadata": {
    "papermill": {
     "duration": 0.012042,
     "end_time": "2023-12-13T16:03:54.174765",
     "exception": false,
     "start_time": "2023-12-13T16:03:54.162723",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "# Policy gradient methods: From REINFORCE to Actor Critic"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5396810f",
   "metadata": {
    "papermill": {
     "duration": 0.011346,
     "end_time": "2023-12-13T16:03:54.197922",
     "exception": false,
     "start_time": "2023-12-13T16:03:54.186576",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "The methods we learned in previous notebooks such as Monte Carlo Methods, TD-learning, and Deep Q-learning learn value functions and use them to learn optimal policy. There exists another category of methods that directly optimize the policy, rather than relying on the estimation of a value function. These methods are known as Policy Gradient Methods.\n",
    "\n",
    "Policy Gradient Methods are especially useful, for example, when the policy is a more straightforward function to approximate compared to the value function. In such case, a policy-based method will typically learn faster and yield a superior asymptotic policy. In the opposite case where a value function may be simpler, estimating the value function might work better. Another important advantage of using policy gradient methods is that we can impose our prior on policy explicitly to construct the desired form of the policy.\n",
    "\n",
    "In this notebook, we will learn three basic policy gradient methods, REINFORCE, REINFORCE with baseline, and Actor Critic. \n",
    "If we can understand the concept of REINFORCE, we would be able to understand the other two just by adding a few improvements to it. \n",
    "We first go over some theoretical concepts to develop an understanding on policy gradient methods and explore the fundamentals of REINFORCE.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6643e73",
   "metadata": {
    "papermill": {
     "duration": 0.011431,
     "end_time": "2023-12-13T16:03:54.221028",
     "exception": false,
     "start_time": "2023-12-13T16:03:54.209597",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "724ec69a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-12-13T16:03:54.246783Z",
     "iopub.status.busy": "2023-12-13T16:03:54.245986Z",
     "iopub.status.idle": "2023-12-13T16:04:13.417023Z",
     "shell.execute_reply": "2023-12-13T16:04:13.415606Z"
    },
    "papermill": {
     "duration": 19.187957,
     "end_time": "2023-12-13T16:04:13.420659",
     "exception": false,
     "start_time": "2023-12-13T16:03:54.232702",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: gymnasium[classic_control] in /opt/conda/lib/python3.10/site-packages (0.29.0)\r\n",
      "Requirement already satisfied: numpy>=1.21.0 in /opt/conda/lib/python3.10/site-packages (from gymnasium[classic_control]) (1.24.3)\r\n",
      "Requirement already satisfied: cloudpickle>=1.2.0 in /opt/conda/lib/python3.10/site-packages (from gymnasium[classic_control]) (2.2.1)\r\n",
      "Requirement already satisfied: typing-extensions>=4.3.0 in /opt/conda/lib/python3.10/site-packages (from gymnasium[classic_control]) (4.5.0)\r\n",
      "Requirement already satisfied: farama-notifications>=0.0.1 in /opt/conda/lib/python3.10/site-packages (from gymnasium[classic_control]) (0.0.4)\r\n",
      "Collecting pygame>=2.1.3 (from gymnasium[classic_control])\r\n",
      "  Obtaining dependency information for pygame>=2.1.3 from https://files.pythonhosted.org/packages/c8/c7/0d77e0e327bf09c12f445f92f5bad0b447375d7b836c5bac5255ead8436f/pygame-2.5.2-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl.metadata\r\n",
      "  Downloading pygame-2.5.2-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl.metadata (13 kB)\r\n",
      "Downloading pygame-2.5.2-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (14.0 MB)\r\n",
      "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m14.0/14.0 MB\u001b[0m \u001b[31m61.7 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\r\n",
      "\u001b[?25hInstalling collected packages: pygame\r\n",
      "Successfully installed pygame-2.5.2\r\n"
     ]
    }
   ],
   "source": [
    "# Import packages\n",
    "!pip install gymnasium[classic_control]\n",
    "\n",
    "import sys\n",
    "import os\n",
    "os.environ['TF_CPP_MIN_LOG_LEVEL'] = '2' # INFO and WARNING messages are not printed\n",
    "\n",
    "import gymnasium as gym\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import tqdm\n",
    "\n",
    "import torch\n",
    "import torch.optim as optim\n",
    "from torch.autograd import Variable\n",
    "import torch.nn.functional as F\n",
    "import torch.nn as nn\n",
    "\n",
    "from IPython.display import clear_output\n",
    "from IPython import display\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "# set random seeds\n",
    "torch.manual_seed(0)\n",
    "np.random.seed(0)\n",
    "\n",
    "# check and use GPU if available if not use CPU\n",
    "device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3192f519",
   "metadata": {
    "papermill": {
     "duration": 0.012962,
     "end_time": "2023-12-13T16:04:13.448042",
     "exception": false,
     "start_time": "2023-12-13T16:04:13.435080",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Prepare environment"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "319b22ca",
   "metadata": {
    "papermill": {
     "duration": 0.013255,
     "end_time": "2023-12-13T16:04:13.474258",
     "exception": false,
     "start_time": "2023-12-13T16:04:13.461003",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "In this notebook, we utilize the CartPole-v0 environment in Gymnasium.\n",
    "\n",
    "[Learn more about the CartPole-v0 environment](https://gymnasium.farama.org/environments/classic_control/cart_pole/)\n",
    "\n",
    "The goal of this environment is to balance a pole by applying forces in the left and right directions on the cart. It has a discrete action space:\n",
    "- 0: Push cart to the left\n",
    "- 1: Push cart to the right\n",
    "\n",
    "Upon taking an action, either left or right, an agent observes a 4-dimensional state consisting of:\n",
    "- Cart Position\n",
    "- Cart Velocity\n",
    "- Pole Angle\n",
    "- Pole Angular Velocity\n",
    "\n",
    "A reward of +1 is granted to the agent at each step while the pole is kept upright. The maximum reward an agent can earn in a single episode is 200.\n",
    "\n",
    "The episode ends under the following conditions:\n",
    "- Termination: Pole Angle is greater than ±12°\n",
    "- Termination: Cart Position is greater than ±2.4 (center of the cart reaches the edge of the display)\n",
    "- Truncation: Episode length exceeds 200 steps\n",
    "\n",
    "In the code below, I provide an example of the agent randomly exploring this environment over 20 time steps.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "98d1198e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-12-13T16:04:13.502696Z",
     "iopub.status.busy": "2023-12-13T16:04:13.502167Z",
     "iopub.status.idle": "2023-12-13T16:04:28.455188Z",
     "shell.execute_reply": "2023-12-13T16:04:28.454214Z"
    },
    "papermill": {
     "duration": 14.970166,
     "end_time": "2023-12-13T16:04:28.457364",
     "exception": false,
     "start_time": "2023-12-13T16:04:13.487198",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create CartPole environment\n",
    "env = gym.make('CartPole-v0', render_mode='rgb_array')\n",
    "state, _ = env.reset()\n",
    "\n",
    "# Run the environment for 20 steps\n",
    "for i in range(20):\n",
    "    # Display the current state of the environment\n",
    "    plt.imshow(env.render())\n",
    "    display.display(plt.gcf())\n",
    "    display.clear_output(wait=True)\n",
    "    \n",
    "    # Choose a random action from the action space\n",
    "    action = env.action_space.sample()\n",
    "    \n",
    "    # Take the chosen action and observe the next state, reward, and termination status\n",
    "    state, reward, terminated, truncated, info = env.step(action)\n",
    "    \n",
    "    # If the episode is terminated or truncated, reset the environment\n",
    "    if terminated or truncated:\n",
    "        state, info = env.reset()\n",
    "\n",
    "# Close the environment after exploration\n",
    "env.close()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ce26ba6",
   "metadata": {
    "papermill": {
     "duration": 0.012526,
     "end_time": "2023-12-13T16:04:28.483089",
     "exception": false,
     "start_time": "2023-12-13T16:04:28.470563",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Policy Gradient Methods Theory"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "272d6ef6",
   "metadata": {
    "papermill": {
     "duration": 0.012952,
     "end_time": "2023-12-13T16:04:28.509241",
     "exception": false,
     "start_time": "2023-12-13T16:04:28.496289",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Policy Gradient Methods directly learn a parameterized policy that can select actions without estimating a value function. In mathematical expression, this means to learn the policy's parameter vector $\\theta$ in the below expression\n",
    "\n",
    "$$\\pi(a|s,\\theta)=P\\{A_t=a|S_t=s, \\theta_t=\\theta\\}$$\n",
    "\n",
    "Here, $\\pi(a|s,\\theta)$ represents the probability of taking action $a$ at time $t$ given that the environment is in state $s$ at that time, with parameter $\\theta$. Since our ultimate objective is to learn the optimal policy, it makes sense to directly optimize and learn it. But how do we achieve this?\n",
    "\n",
    "A common approach is to define a model, such as a neural network, as a policy estimator. This model outputs an action probability distribution given a state. But what would be the objective function to optimize the parameter vector $\\theta$?\n",
    "\n",
    "For example, with Deep Q-learning (which is one of the value function estimation methods), we use Temporal Difference (TD) error to update the value function\n",
    "\n",
    "$$ (R_{t+1} + \\gamma \\max_a Q_{\\theta}(S_{t+1}, a)) - Q_{\\theta^-}(S_t, A_t) $$\n",
    "\n",
    "where $\\theta$ is the parameters of the value function estimate and $\\theta^-$ is the parameters of the target network, which are less frequently updated. By running backpropagation with this objective function, we can optimize the model estimating a value function. For more details, you can refer to [this notebook](https://www.kaggle.com/code/minaiyuki/deep-q-learning-dqn-tutorial-with-cartpole-v0).\n",
    "\n",
    "For policy gradient methods, we can consider that the objective is a discounted return we can gain through adopting the policy. We run an optimization process to maximize this objective function.\n",
    "\n",
    "Can we compute the gradient of this return? No, we don't exactly know the form of a return or reward function so we cannot directly compute the gradient. But **Policy Gradient Theorem** offers a way to compute the gradient of this function. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a242b2f0",
   "metadata": {
    "papermill": {
     "duration": 0.012539,
     "end_time": "2023-12-13T16:04:28.534869",
     "exception": false,
     "start_time": "2023-12-13T16:04:28.522330",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "### Policy Gradient Theorem"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7a51d79",
   "metadata": {
    "papermill": {
     "duration": 0.012424,
     "end_time": "2023-12-13T16:04:28.560356",
     "exception": false,
     "start_time": "2023-12-13T16:04:28.547932",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "The Policy Gradient Theorem provides an analytic expression for the gradient of an objective (such as return) with respect to the policy parameter. Let's denote the objective function we would like to maximize as $J(\\theta)$.\n",
    "Then, the policy gradient theorem provides the estimate of the derivative of this function as follows:\n",
    "\n",
    "$$ \\nabla J(\\theta) \\propto \\sum_s \\mu(s) \\sum_a q_{\\pi}(s,a) \\nabla \\pi(a|s, \\theta) $$\n",
    "\n",
    "where $\\nabla J(\\theta)$ represents the gradient with respect to $\\theta$, $\\pi$ denotes the policy corersponding to parameter vector $\\theta$, and $q_{\\pi}(s,a)$ denotes the value of a state action pair under policy $\\pi$. $\\mu$ is the distribution of state $s$ under $\\pi$. \n",
    "The detailed proof is offered in p.325 of Ref or this [link](https://lilianweng.github.io/posts/2018-04-08-policy-gradient/).\n",
    "\n",
    "Let's think about what this expression means. \n",
    "Remember that our goal is to maximize the objective function $J(\\theta)$. So we would like to perform gradient ascent with respect to $\\theta$. \n",
    "When a value of action $a$ under state $s$ is large (i.e. when $q_{\\pi}(s,a)$ is a large value), we would like to make this action more likely because we can gain a large return. To achieve this, we multiply the derivative term $\\nabla \\pi(a|s, \\theta)$ with this large estimated value of this state to move largely toward this gradient ascent direction. This causes this action to happen more likely.\n",
    "On the other hand, when the value of action $a$ under $s$ is a small value (or even a negative value), we move the gradient ascent direction with a smaller step (or move away from this direction) and don't increase the probability of taking this action much (or reduce the probability of taking this action).\n",
    "\n",
    "The first term $\\sum_s \\mu(s)$ controls the weight of each state. States that are more often visited have larger weights on the update of $\\theta$ compared to the states that are rarely visited.\n",
    "\n",
    "By iterating this update of $\\theta$, the algorithm learns which ascent direction it should go and gradually learns which action it should maximize the probability to maximize the objective function (i.e. return). \n",
    "\n",
    "By the way, the proportionality (not equality) is all that is needed to perform a policy gradient update because any constant of proportionality can be absorbed into the step size $\\alpha$, which is otherwise arbitrary. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f86fb52c",
   "metadata": {
    "papermill": {
     "duration": 0.01268,
     "end_time": "2023-12-13T16:04:28.586255",
     "exception": false,
     "start_time": "2023-12-13T16:04:28.573575",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## REINFORCE"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39104aff",
   "metadata": {
    "papermill": {
     "duration": 0.012492,
     "end_time": "2023-12-13T16:04:28.611845",
     "exception": false,
     "start_time": "2023-12-13T16:04:28.599353",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Now, let's learn about the most basic policy gradient algorithm: REINFORCE. \n",
    "The Policy Gradient Theorem has a term  $\\sum_s \\mu(s)$ to account for how often the states occur under the target policy $\\pi$. If policy $\\pi$ is followed, then states will be encountered in the same proportions as policy $\\mu(s)$. Thus we can rewrite the above expression as follows based on our sampled experience $S_t$:\n",
    "\n",
    "\\begin{align*}\n",
    "\\nabla J(\\theta) &\\propto \\sum_s \\mu(s) \\sum_a q_{\\pi}(s,a) \\nabla \\pi(a|s, \\theta) \\\\\n",
    "&= \\mathbb{E}_{\\pi} [\\sum_a q_{\\pi}(S_t, a) \\nabla\\pi(a|S_t,\\theta)]\n",
    "\\end{align*}\n",
    "\n",
    "\n",
    "With this expression, we can write our gradient ascent with sampled experience as follows:\n",
    "\n",
    "$$\\theta_{t+1}=\\theta_t + \\alpha\\sum_a \\tilde{q_{\\pi}}(S_t, a) \\nabla\\pi(a|S_t,\\theta)$$\n",
    "\n",
    "where $\\tilde{q_{\\pi}}$ is some learned approximation of $q_{\\pi}$. The different algorithm uses a different estimate of this value function but for REINFORCE, it uses discounted return $G_t$ as an estimate of $q_{\\pi}$ as in Monte Carlo Methods. \n",
    "\n",
    "To compute this update equation based on the discounted return $G_t$, we want to make one more change. The above equation involves sum over all actions but we would like to replace it with action $A_t$ we sampled at time step t. Then, we can approximate the value $q_{\\pi}(S_t, A_t)$ with the observed discounted return after visiting a state-action pair $(S_t, A_t)$. How can we make this change?\n",
    "Just with a few lines of math, we can rewrite the above gradient equation as follows:\n",
    "\n",
    "\n",
    "\\begin{align*}\n",
    "\\nabla J(\\theta) &\\propto \\sum_s \\mu(s) \\sum_a q_{\\pi}(s,a) \\nabla \\pi(a|s, \\theta) \\\\\n",
    "&= \\mathbb{E}_{\\pi} [\\sum_a q_{\\pi}(S_t, a) \\nabla\\pi(a|S_t,\\theta)] \\\\\n",
    "&= \\mathbb{E}_{\\pi} [\\sum_a \\pi(a|S_t,\\theta) q_{\\pi}(S_t, a) \\frac{\\nabla\\pi(a|S_t,\\theta)}{\\pi(a|S_t,\\theta)}] \\quad (\\text{multiplied by } \\frac{\\pi(a|S_t,\\theta)}{\\pi(a|S_t,\\theta)}) \\\\\n",
    "&= \\mathbb{E}_{\\pi} [q_{\\pi}(S_t, A_t) \\frac{\\nabla\\pi(A_t|S_t,\\theta)}{\\pi(A_t|S_t,\\theta)}] \\quad (\\text{replacing sum over } a \\text{ by the expectation over sample } A_t \\sim \\pi) \\\\\n",
    "&= \\mathbb{E}_{\\pi} [G_t \\frac{\\nabla\\pi(A_t|S_t,\\theta)}{\\pi(A_t|S_t,\\theta)}] \\quad (\\text{replacing } q \\text{ value estimate as } G_t \\text{ because } \\mathbb{E}_{\\pi}[G_t|S_t,A_t]=q_{\\pi}(S_t,A_t))\n",
    "\\end{align*}\n",
    "\n",
    "Here, as we replaced the summation over all states with the expectation in the above section, we used a similar trick to replace the summation over all actions with the expectation. At each step, we observe $G_t$ following $\\pi$. By collecting many steps, the average of observed $G_t$ will converge to the true value $q_{\\pi}(s,a)$. \n",
    "\n",
    "In summary, the gradient equation we use for REINFORCE is defined as follows:\n",
    "\n",
    "\\begin{align*}\n",
    "\\theta_{t+1} &= \\theta_t + \\alpha G_t \\frac{\\nabla\\pi(A_t|S_t,\\theta)}{\\pi(A_t|S_t,\\theta)} \\\\\n",
    "&= \\theta_t + \\alpha G_t \\nabla \\ln \\pi(A_t|S_t,\\theta) \\quad (\\text{by } \\nabla\\ln x=\\frac{\\nabla x}{x})\n",
    "\\end{align*}\n",
    "\n",
    "Let's interpret this equation a little bit more. The update increases the parameter vector in the direction proportional to the return, and inversely proportional to the action probability. \n",
    "The former suggests that it moves the parameters in the directions that favor actions that yield the higher return. The latter controls the gradient update for frequently observed actions not to be at an advantage. The update will be more often in their direction, so without this term, the frequently observed actions might win out even if they do not yield the highest return.\n",
    "\n",
    "Note that as REINFORCE uses return $G_t$, the update has to wait until the end of the episode. Without the completion of the episode, the update cannot happen like Monte Carlo Methods.\n",
    "\n",
    "Below is the pseudo-code of REINFORCE (a.k.a. Monte Carlo Policy Gradient Algorithm).\n"
   ]
  },
  {
   "attachments": {
    "image-3.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "13d2c9f8",
   "metadata": {
    "papermill": {
     "duration": 0.012562,
     "end_time": "2023-12-13T16:04:28.637323",
     "exception": false,
     "start_time": "2023-12-13T16:04:28.624761",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "![image-3.png](attachment:image-3.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "483ea535",
   "metadata": {
    "papermill": {
     "duration": 0.01248,
     "end_time": "2023-12-13T16:04:28.662865",
     "exception": false,
     "start_time": "2023-12-13T16:04:28.650385",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Let's implement this algorithm. First, we define our model to estimate the policy. In this tutorial, we use a simple neural network model as a policy estimator.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7e6dd2f1",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-12-13T16:04:28.690160Z",
     "iopub.status.busy": "2023-12-13T16:04:28.689760Z",
     "iopub.status.idle": "2023-12-13T16:04:28.699527Z",
     "shell.execute_reply": "2023-12-13T16:04:28.698759Z"
    },
    "papermill": {
     "duration": 0.025775,
     "end_time": "2023-12-13T16:04:28.701448",
     "exception": false,
     "start_time": "2023-12-13T16:04:28.675673",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "class NeuralNet(torch.nn.Module):\n",
    "    def __init__(self, input_size, output_size, activation, layers=[32,32,16]):\n",
    "        super().__init__()\n",
    "\n",
    "        # Define layers with ReLU activation\n",
    "        self.linear1 = torch.nn.Linear(input_size, layers[0])\n",
    "        self.activation1 = torch.nn.ReLU()\n",
    "        self.linear2 = torch.nn.Linear(layers[0], layers[1])\n",
    "        self.activation2 = torch.nn.ReLU()\n",
    "        self.linear3 = torch.nn.Linear(layers[1], layers[2])\n",
    "        self.activation3 = torch.nn.ReLU()\n",
    "\n",
    "        self.output_layer = torch.nn.Linear(layers[2], output_size)\n",
    "        self.output_activation = activation\n",
    "\n",
    "        # Initialization using Xavier normal (a popular technique for initializing weights in NNs)\n",
    "        torch.nn.init.xavier_normal_(self.linear1.weight)\n",
    "        torch.nn.init.xavier_normal_(self.linear2.weight)\n",
    "        torch.nn.init.xavier_normal_(self.linear3.weight)\n",
    "        torch.nn.init.xavier_normal_(self.output_layer.weight)\n",
    "\n",
    "    def forward(self, inputs):\n",
    "        # Forward pass through the layers\n",
    "        x = self.activation1(self.linear1(inputs))\n",
    "        x = self.activation2(self.linear2(x))\n",
    "        x = self.activation3(self.linear3(x))\n",
    "        x = self.output_activation(self.output_layer(x))\n",
    "        return x\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88ca9429",
   "metadata": {
    "papermill": {
     "duration": 0.012471,
     "end_time": "2023-12-13T16:04:28.726912",
     "exception": false,
     "start_time": "2023-12-13T16:04:28.714441",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Next, we prepare helper functions to generate an episode following the current policy model and evaluate the performance of the current policy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5545de07",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-12-13T16:04:28.753980Z",
     "iopub.status.busy": "2023-12-13T16:04:28.753615Z",
     "iopub.status.idle": "2023-12-13T16:04:28.764114Z",
     "shell.execute_reply": "2023-12-13T16:04:28.763006Z"
    },
    "papermill": {
     "duration": 0.026664,
     "end_time": "2023-12-13T16:04:28.766329",
     "exception": false,
     "start_time": "2023-12-13T16:04:28.739665",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "def generate_episode(env, policy_net):\n",
    "    \"\"\"\n",
    "    Generates an episode by executing the current policy in the given env\n",
    "    \"\"\"\n",
    "    states = []\n",
    "    actions = []\n",
    "    rewards = []\n",
    "    log_probs = []\n",
    "    max_t = 1000 # max horizon of one episode\n",
    "    state, _ = env.reset()\n",
    "    for t in range(max_t):\n",
    "        state = torch.from_numpy(state).float().unsqueeze(0)\n",
    "        probs = policy_net.forward(Variable(state)) # get each action choice probability with the current policy network\n",
    "        action = np.random.choice(env.action_space.n, p=np.squeeze(probs.detach().numpy())) # probablistic\n",
    "        # action = np.argmax(probs.detach().numpy()) # greedy\n",
    "        \n",
    "        # compute the log_prob to use this in parameter update\n",
    "        log_prob = torch.log(probs.squeeze(0)[action])\n",
    "        \n",
    "        # append values\n",
    "        states.append(state)\n",
    "        actions.append(action)\n",
    "        log_probs.append(log_prob)\n",
    "        \n",
    "        # take a selected action\n",
    "        state, reward, terminated, truncated, _ = env.step(action)\n",
    "        rewards.append(reward)\n",
    "\n",
    "        if terminated | truncated:\n",
    "            break\n",
    "            \n",
    "    return states, actions, rewards, log_probs\n",
    "\n",
    "\n",
    "def evaluate_policy(env, policy_net):\n",
    "    \"\"\"\n",
    "    Compute accumulative trajectory reward\n",
    "    \"\"\"\n",
    "    states, actions, rewards, log_probs = generate_episode(env, policy_net)\n",
    "    return np.sum(rewards)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "159a96ab",
   "metadata": {
    "papermill": {
     "duration": 0.012358,
     "end_time": "2023-12-13T16:04:28.791825",
     "exception": false,
     "start_time": "2023-12-13T16:04:28.779467",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Lastly, we implement a function to train the policy neural network. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "200b087f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-12-13T16:04:28.819293Z",
     "iopub.status.busy": "2023-12-13T16:04:28.818327Z",
     "iopub.status.idle": "2023-12-13T16:04:28.826327Z",
     "shell.execute_reply": "2023-12-13T16:04:28.825524Z"
    },
    "papermill": {
     "duration": 0.024016,
     "end_time": "2023-12-13T16:04:28.828450",
     "exception": false,
     "start_time": "2023-12-13T16:04:28.804434",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "def train_REINRORCE(env, policy_net, policy_optimizer, gamma=0.99):\n",
    "    \"\"\"\n",
    "    Trains the policy network on a single episode using REINFORCE\n",
    "    \"\"\"\n",
    "    # Generate an episode with the current policy network\n",
    "    states, actions, rewards, log_probs = generate_episode(env, policy_net)\n",
    "    T = len(states)\n",
    "\n",
    "    # Compute total discounted return at each time step\n",
    "    Gs = []\n",
    "    G = 0\n",
    "    for t in range(T-1,-1,-1): # iterate in backward order to make the computation easier\n",
    "        G = rewards[t] + gamma*G\n",
    "        Gs.insert(0,G)        \n",
    "\n",
    "    # Compute objective function value L(theta)\n",
    "    L_theta = []\n",
    "    for log_prob, G in zip(log_probs, Gs):\n",
    "        L_theta.append(-log_prob * G * 1/T) # to perform a gradient ascent, compute the negative objective value (minimizing this value-> maximizing the original objective value)\n",
    "    L_theta = torch.stack(L_theta).sum() # accumulate all gradient to perform one update for one episode (not at every time step)\n",
    "\n",
    "    # Update policy\n",
    "    policy_optimizer.zero_grad() # reset all gradients to zero\n",
    "    L_theta.backward() # compute the gradient\n",
    "    policy_optimizer.step() # update the parameters (gradient descent)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5659e8a5",
   "metadata": {
    "papermill": {
     "duration": 0.012362,
     "end_time": "2023-12-13T16:04:28.853626",
     "exception": false,
     "start_time": "2023-12-13T16:04:28.841264",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Let's test whether REINFORCE can learn a good policy to solve the cart pole environment. In the below code, we train the policy network for 3,500 episodes using 5 different random seeds. To monitor learning progress, we freeze the network weights every 100 episodes and perform 20 episodes with the current policy, evaluating the test performance of the policy at each training phase. \n",
    "\n",
    "Note: The below code may take about 10 min to run.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "1a491343",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-12-13T16:04:28.936527Z",
     "iopub.status.busy": "2023-12-13T16:04:28.935843Z",
     "iopub.status.idle": "2023-12-13T16:04:28.942626Z",
     "shell.execute_reply": "2023-12-13T16:04:28.941848Z"
    },
    "papermill": {
     "duration": 0.02357,
     "end_time": "2023-12-13T16:04:28.944644",
     "exception": false,
     "start_time": "2023-12-13T16:04:28.921074",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Define parameter values\n",
    "env_name = 'CartPole-v0'\n",
    "num_episodes = 3500\n",
    "policy_lr = 5e-4 # policy network's learning rate\n",
    "num_seeds = 5 # fit model with 5 different seeds and plot average performance of 5 seeds\n",
    "l = num_episodes//100 # use to create x label for plot\n",
    "returns = np.zeros((num_seeds, l)) # dim: (5 ,35)\n",
    "gamma = 0.99 # discount factor\n",
    "\n",
    "# Create the environment.\n",
    "env = gym.make(env_name)\n",
    "nA = env.action_space.n\n",
    "nS = 4\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "5dcacc41",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-12-13T16:04:28.972633Z",
     "iopub.status.busy": "2023-12-13T16:04:28.971952Z",
     "iopub.status.idle": "2023-12-13T16:29:04.192717Z",
     "shell.execute_reply": "2023-12-13T16:29:04.191525Z"
    },
    "papermill": {
     "duration": 1475.237793,
     "end_time": "2023-12-13T16:29:04.195533",
     "exception": false,
     "start_time": "2023-12-13T16:04:28.957740",
     "status": "completed"
    },
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/5 [00:00<?, ?it/s]/tmp/ipykernel_19/332058975.py:27: UserWarning: Implicit dimension choice for softmax has been deprecated. Change the call to include dim=X as an argument.\n",
      "  x = self.output_activation(self.output_layer(x))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode: 0\n",
      "The avg. test return for episode 0 is 19.55 with std. of 9.728694670920657.\n",
      "Episode: 100\n",
      "The avg. test return for episode 100 is 26.15 with std. of 11.892329460622927.\n",
      "Episode: 200\n",
      "The avg. test return for episode 200 is 18.15 with std. of 8.070161088850705.\n",
      "Episode: 300\n",
      "The avg. test return for episode 300 is 23.7 with std. of 11.92937550754439.\n",
      "Episode: 400\n",
      "The avg. test return for episode 400 is 22.7 with std. of 10.663489110042734.\n",
      "Episode: 500\n",
      "The avg. test return for episode 500 is 22.45 with std. of 13.948028534527737.\n",
      "Episode: 600\n",
      "The avg. test return for episode 600 is 30.65 with std. of 15.834377158574949.\n",
      "Episode: 700\n",
      "The avg. test return for episode 700 is 36.65 with std. of 24.827958031219563.\n",
      "Episode: 800\n",
      "The avg. test return for episode 800 is 31.35 with std. of 14.004552831133166.\n",
      "Episode: 900\n",
      "The avg. test return for episode 900 is 58.7 with std. of 29.37873380525444.\n",
      "Episode: 1000\n",
      "The avg. test return for episode 1000 is 66.95 with std. of 42.297133472612536.\n",
      "Episode: 1100\n",
      "The avg. test return for episode 1100 is 125.45 with std. of 46.63097146746998.\n",
      "Episode: 1200\n",
      "The avg. test return for episode 1200 is 179.6 with std. of 30.71872393183024.\n",
      "Episode: 1300\n",
      "The avg. test return for episode 1300 is 164.95 with std. of 29.670650481578594.\n",
      "Episode: 1400\n",
      "The avg. test return for episode 1400 is 99.45 with std. of 54.81101622849188.\n",
      "Episode: 1500\n",
      "The avg. test return for episode 1500 is 149.3 with std. of 34.6844345492326.\n",
      "Episode: 1600\n",
      "The avg. test return for episode 1600 is 179.95 with std. of 37.4091900473667.\n",
      "Episode: 1700\n",
      "The avg. test return for episode 1700 is 188.25 with std. of 36.03869448245871.\n",
      "Episode: 1800\n",
      "The avg. test return for episode 1800 is 196.85 with std. of 11.641627893039702.\n",
      "Episode: 1900\n",
      "The avg. test return for episode 1900 is 104.65 with std. of 37.60754578538727.\n",
      "Episode: 2000\n",
      "The avg. test return for episode 2000 is 171.6 with std. of 34.74248120097354.\n",
      "Episode: 2100\n",
      "The avg. test return for episode 2100 is 180.2 with std. of 25.500196077677522.\n",
      "Episode: 2200\n",
      "The avg. test return for episode 2200 is 184.5 with std. of 22.95539152356152.\n",
      "Episode: 2300\n",
      "The avg. test return for episode 2300 is 196.25 with std. of 16.345871038277526.\n",
      "Episode: 2400\n",
      "The avg. test return for episode 2400 is 200.0 with std. of 0.0.\n",
      "Episode: 2500\n",
      "The avg. test return for episode 2500 is 200.0 with std. of 0.0.\n",
      "Episode: 2600\n",
      "The avg. test return for episode 2600 is 194.75 with std. of 11.19765600471813.\n",
      "Episode: 2700\n",
      "The avg. test return for episode 2700 is 129.15 with std. of 27.46684364829712.\n",
      "Episode: 2800\n",
      "The avg. test return for episode 2800 is 194.7 with std. of 8.983874442577656.\n",
      "Episode: 2900\n",
      "The avg. test return for episode 2900 is 197.15 with std. of 8.895363961075454.\n",
      "Episode: 3000\n",
      "The avg. test return for episode 3000 is 162.5 with std. of 19.30932417253385.\n",
      "Episode: 3100\n",
      "The avg. test return for episode 3100 is 198.3 with std. of 5.441507144165117.\n",
      "Episode: 3200\n",
      "The avg. test return for episode 3200 is 197.45 with std. of 9.085565474971824.\n",
      "Episode: 3300\n",
      "The avg. test return for episode 3300 is 200.0 with std. of 0.0.\n",
      "Episode: 3400\n",
      "The avg. test return for episode 3400 is 199.55 with std. of 1.9615045245933027.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 20%|██        | 1/5 [05:01<20:06, 301.53s/it]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode: 0\n",
      "The avg. test return for episode 0 is 20.6 with std. of 8.674099376880577.\n",
      "Episode: 100\n",
      "The avg. test return for episode 100 is 23.85 with std. of 10.946574806760333.\n",
      "Episode: 200\n",
      "The avg. test return for episode 200 is 21.15 with std. of 7.3230799531344735.\n",
      "Episode: 300\n",
      "The avg. test return for episode 300 is 23.95 with std. of 10.346376177193635.\n",
      "Episode: 400\n",
      "The avg. test return for episode 400 is 30.7 with std. of 20.714970432032963.\n",
      "Episode: 500\n",
      "The avg. test return for episode 500 is 29.65 with std. of 16.51446335791751.\n",
      "Episode: 600\n",
      "The avg. test return for episode 600 is 40.7 with std. of 19.940160480798543.\n",
      "Episode: 700\n",
      "The avg. test return for episode 700 is 37.7 with std. of 30.01849429934819.\n",
      "Episode: 800\n",
      "The avg. test return for episode 800 is 39.2 with std. of 19.216139050287914.\n",
      "Episode: 900\n",
      "The avg. test return for episode 900 is 64.35 with std. of 32.85464198557032.\n",
      "Episode: 1000\n",
      "The avg. test return for episode 1000 is 86.5 with std. of 49.999499997499974.\n",
      "Episode: 1100\n",
      "The avg. test return for episode 1100 is 99.75 with std. of 41.5630545075792.\n",
      "Episode: 1200\n",
      "The avg. test return for episode 1200 is 151.2 with std. of 50.13840843106211.\n",
      "Episode: 1300\n",
      "The avg. test return for episode 1300 is 175.65 with std. of 43.38234087736622.\n",
      "Episode: 1400\n",
      "The avg. test return for episode 1400 is 92.5 with std. of 35.802932840760405.\n",
      "Episode: 1500\n",
      "The avg. test return for episode 1500 is 144.85 with std. of 30.387949914398632.\n",
      "Episode: 1600\n",
      "The avg. test return for episode 1600 is 171.35 with std. of 24.45664531369746.\n",
      "Episode: 1700\n",
      "The avg. test return for episode 1700 is 154.55 with std. of 29.7329362828497.\n",
      "Episode: 1800\n",
      "The avg. test return for episode 1800 is 191.6 with std. of 18.268552214119214.\n",
      "Episode: 1900\n",
      "The avg. test return for episode 1900 is 200.0 with std. of 0.0.\n",
      "Episode: 2000\n",
      "The avg. test return for episode 2000 is 118.55 with std. of 26.984208344882013.\n",
      "Episode: 2100\n",
      "The avg. test return for episode 2100 is 120.55 with std. of 30.59652758075661.\n",
      "Episode: 2200\n",
      "The avg. test return for episode 2200 is 186.0 with std. of 25.68462575160479.\n",
      "Episode: 2300\n",
      "The avg. test return for episode 2300 is 200.0 with std. of 0.0.\n",
      "Episode: 2400\n",
      "The avg. test return for episode 2400 is 196.35 with std. of 15.909981143923458.\n",
      "Episode: 2500\n",
      "The avg. test return for episode 2500 is 200.0 with std. of 0.0.\n",
      "Episode: 2600\n",
      "The avg. test return for episode 2600 is 138.1 with std. of 15.58813651467038.\n",
      "Episode: 2700\n",
      "The avg. test return for episode 2700 is 125.3 with std. of 16.95906837063876.\n",
      "Episode: 2800\n",
      "The avg. test return for episode 2800 is 73.6 with std. of 33.15177219998956.\n",
      "Episode: 2900\n",
      "The avg. test return for episode 2900 is 117.5 with std. of 11.508692367076288.\n",
      "Episode: 3000\n",
      "The avg. test return for episode 3000 is 193.05 with std. of 15.265893357416067.\n",
      "Episode: 3100\n",
      "The avg. test return for episode 3100 is 200.0 with std. of 0.0.\n",
      "Episode: 3200\n",
      "The avg. test return for episode 3200 is 200.0 with std. of 0.0.\n",
      "Episode: 3300\n",
      "The avg. test return for episode 3300 is 161.55 with std. of 26.312497030878696.\n",
      "Episode: 3400\n",
      "The avg. test return for episode 3400 is 101.2 with std. of 37.919124462466165.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 40%|████      | 2/5 [09:39<14:22, 287.48s/it]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode: 0\n",
      "The avg. test return for episode 0 is 22.15 with std. of 7.747741606429579.\n",
      "Episode: 100\n",
      "The avg. test return for episode 100 is 21.6 with std. of 11.52128465059344.\n",
      "Episode: 200\n",
      "The avg. test return for episode 200 is 22.5 with std. of 9.162423260251623.\n",
      "Episode: 300\n",
      "The avg. test return for episode 300 is 28.8 with std. of 14.445068362593512.\n",
      "Episode: 400\n",
      "The avg. test return for episode 400 is 26.35 with std. of 11.10979297736911.\n",
      "Episode: 500\n",
      "The avg. test return for episode 500 is 28.55 with std. of 9.927109347639925.\n",
      "Episode: 600\n",
      "The avg. test return for episode 600 is 44.15 with std. of 23.057048813757586.\n",
      "Episode: 700\n",
      "The avg. test return for episode 700 is 56.1 with std. of 30.73743645784404.\n",
      "Episode: 800\n",
      "The avg. test return for episode 800 is 66.8 with std. of 41.80621963296849.\n",
      "Episode: 900\n",
      "The avg. test return for episode 900 is 144.55 with std. of 39.62887205056435.\n",
      "Episode: 1000\n",
      "The avg. test return for episode 1000 is 138.85 with std. of 55.02206375627872.\n",
      "Episode: 1100\n",
      "The avg. test return for episode 1100 is 158.45 with std. of 45.70281719981822.\n",
      "Episode: 1200\n",
      "The avg. test return for episode 1200 is 118.35 with std. of 49.946246105187925.\n",
      "Episode: 1300\n",
      "The avg. test return for episode 1300 is 160.55 with std. of 31.161635066215638.\n",
      "Episode: 1400\n",
      "The avg. test return for episode 1400 is 108.4 with std. of 37.022155528818146.\n",
      "Episode: 1500\n",
      "The avg. test return for episode 1500 is 95.1 with std. of 31.821219335531442.\n",
      "Episode: 1600\n",
      "The avg. test return for episode 1600 is 196.55 with std. of 9.32992497290305.\n",
      "Episode: 1700\n",
      "The avg. test return for episode 1700 is 88.05 with std. of 32.7467173927403.\n",
      "Episode: 1800\n",
      "The avg. test return for episode 1800 is 200.0 with std. of 0.0.\n",
      "Episode: 1900\n",
      "The avg. test return for episode 1900 is 199.8 with std. of 0.8717797887081347.\n",
      "Episode: 2000\n",
      "The avg. test return for episode 2000 is 195.75 with std. of 11.170832556260075.\n",
      "Episode: 2100\n",
      "The avg. test return for episode 2100 is 194.95 with std. of 17.313217494157463.\n",
      "Episode: 2200\n",
      "The avg. test return for episode 2200 is 92.45 with std. of 31.900587768879742.\n",
      "Episode: 2300\n",
      "The avg. test return for episode 2300 is 103.8 with std. of 30.92668750448389.\n",
      "Episode: 2400\n",
      "The avg. test return for episode 2400 is 144.95 with std. of 19.73442423786415.\n",
      "Episode: 2500\n",
      "The avg. test return for episode 2500 is 129.25 with std. of 11.202120335008011.\n",
      "Episode: 2600\n",
      "The avg. test return for episode 2600 is 136.9 with std. of 18.23156603257109.\n",
      "Episode: 2700\n",
      "The avg. test return for episode 2700 is 124.35 with std. of 12.693600749984222.\n",
      "Episode: 2800\n",
      "The avg. test return for episode 2800 is 119.9 with std. of 11.28228700219951.\n",
      "Episode: 2900\n",
      "The avg. test return for episode 2900 is 77.2 with std. of 31.454093533274808.\n",
      "Episode: 3000\n",
      "The avg. test return for episode 3000 is 105.45 with std. of 6.127601488347622.\n",
      "Episode: 3100\n",
      "The avg. test return for episode 3100 is 158.35 with std. of 16.93893444110343.\n",
      "Episode: 3200\n",
      "The avg. test return for episode 3200 is 198.15 with std. of 4.257640191467569.\n",
      "Episode: 3300\n",
      "The avg. test return for episode 3300 is 166.85 with std. of 14.371064678721615.\n",
      "Episode: 3400\n",
      "The avg. test return for episode 3400 is 171.1 with std. of 12.922461065911556.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 60%|██████    | 3/5 [14:19<09:28, 284.06s/it]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode: 0\n",
      "The avg. test return for episode 0 is 16.35 with std. of 6.060321773635456.\n",
      "Episode: 100\n",
      "The avg. test return for episode 100 is 19.65 with std. of 6.381810088054956.\n",
      "Episode: 200\n",
      "The avg. test return for episode 200 is 28.35 with std. of 13.085392619252968.\n",
      "Episode: 300\n",
      "The avg. test return for episode 300 is 27.4 with std. of 15.656947339759435.\n",
      "Episode: 400\n",
      "The avg. test return for episode 400 is 31.0 with std. of 14.184498581197715.\n",
      "Episode: 500\n",
      "The avg. test return for episode 500 is 39.85 with std. of 20.794891199523022.\n",
      "Episode: 600\n",
      "The avg. test return for episode 600 is 43.2 with std. of 22.15761720041214.\n",
      "Episode: 700\n",
      "The avg. test return for episode 700 is 50.05 with std. of 29.35383279914226.\n",
      "Episode: 800\n",
      "The avg. test return for episode 800 is 40.25 with std. of 17.13439523298094.\n",
      "Episode: 900\n",
      "The avg. test return for episode 900 is 78.3 with std. of 34.793821290568246.\n",
      "Episode: 1000\n",
      "The avg. test return for episode 1000 is 80.15 with std. of 43.87285607297524.\n",
      "Episode: 1100\n",
      "The avg. test return for episode 1100 is 117.05 with std. of 49.54641763033933.\n",
      "Episode: 1200\n",
      "The avg. test return for episode 1200 is 167.1 with std. of 39.8684085461158.\n",
      "Episode: 1300\n",
      "The avg. test return for episode 1300 is 144.95 with std. of 23.393321696586828.\n",
      "Episode: 1400\n",
      "The avg. test return for episode 1400 is 193.45 with std. of 16.61467724633855.\n",
      "Episode: 1500\n",
      "The avg. test return for episode 1500 is 194.7 with std. of 10.872442227944925.\n",
      "Episode: 1600\n",
      "The avg. test return for episode 1600 is 192.3 with std. of 17.372679701185998.\n",
      "Episode: 1700\n",
      "The avg. test return for episode 1700 is 200.0 with std. of 0.0.\n",
      "Episode: 1800\n",
      "The avg. test return for episode 1800 is 168.9 with std. of 25.236679654819888.\n",
      "Episode: 1900\n",
      "The avg. test return for episode 1900 is 175.8 with std. of 25.753834665928878.\n",
      "Episode: 2000\n",
      "The avg. test return for episode 2000 is 200.0 with std. of 0.0.\n",
      "Episode: 2100\n",
      "The avg. test return for episode 2100 is 194.95 with std. of 22.012439664880404.\n",
      "Episode: 2200\n",
      "The avg. test return for episode 2200 is 118.55 with std. of 19.22881951654859.\n",
      "Episode: 2300\n",
      "The avg. test return for episode 2300 is 79.5 with std. of 29.914043524739345.\n",
      "Episode: 2400\n",
      "The avg. test return for episode 2400 is 78.1 with std. of 27.06270496458179.\n",
      "Episode: 2500\n",
      "The avg. test return for episode 2500 is 104.85 with std. of 20.42125118595822.\n",
      "Episode: 2600\n",
      "The avg. test return for episode 2600 is 113.4 with std. of 22.050850323740352.\n",
      "Episode: 2700\n",
      "The avg. test return for episode 2700 is 171.7 with std. of 19.725871336901697.\n",
      "Episode: 2800\n",
      "The avg. test return for episode 2800 is 200.0 with std. of 0.0.\n",
      "Episode: 2900\n",
      "The avg. test return for episode 2900 is 200.0 with std. of 0.0.\n",
      "Episode: 3000\n",
      "The avg. test return for episode 3000 is 200.0 with std. of 0.0.\n",
      "Episode: 3100\n",
      "The avg. test return for episode 3100 is 200.0 with std. of 0.0.\n",
      "Episode: 3200\n",
      "The avg. test return for episode 3200 is 200.0 with std. of 0.0.\n",
      "Episode: 3300\n",
      "The avg. test return for episode 3300 is 193.8 with std. of 14.465821787924805.\n",
      "Episode: 3400\n",
      "The avg. test return for episode 3400 is 197.8 with std. of 9.589577675789482.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 80%|████████  | 4/5 [19:26<04:53, 293.24s/it]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode: 0\n",
      "The avg. test return for episode 0 is 17.85 with std. of 8.076354375583081.\n",
      "Episode: 100\n",
      "The avg. test return for episode 100 is 18.25 with std. of 6.425534997181169.\n",
      "Episode: 200\n",
      "The avg. test return for episode 200 is 23.5 with std. of 13.024976007655447.\n",
      "Episode: 300\n",
      "The avg. test return for episode 300 is 23.6 with std. of 12.7216351150314.\n",
      "Episode: 400\n",
      "The avg. test return for episode 400 is 28.45 with std. of 14.674723166043028.\n",
      "Episode: 500\n",
      "The avg. test return for episode 500 is 28.35 with std. of 15.202878017007174.\n",
      "Episode: 600\n",
      "The avg. test return for episode 600 is 27.55 with std. of 14.115505658671955.\n",
      "Episode: 700\n",
      "The avg. test return for episode 700 is 35.7 with std. of 19.0370691021491.\n",
      "Episode: 800\n",
      "The avg. test return for episode 800 is 32.85 with std. of 15.837534530349098.\n",
      "Episode: 900\n",
      "The avg. test return for episode 900 is 55.7 with std. of 21.321585306913743.\n",
      "Episode: 1000\n",
      "The avg. test return for episode 1000 is 50.95 with std. of 20.59484158715478.\n",
      "Episode: 1100\n",
      "The avg. test return for episode 1100 is 71.55 with std. of 34.840314292497425.\n",
      "Episode: 1200\n",
      "The avg. test return for episode 1200 is 126.65 with std. of 57.62315072954619.\n",
      "Episode: 1300\n",
      "The avg. test return for episode 1300 is 165.45 with std. of 45.67217424209186.\n",
      "Episode: 1400\n",
      "The avg. test return for episode 1400 is 163.4 with std. of 46.93548763995107.\n",
      "Episode: 1500\n",
      "The avg. test return for episode 1500 is 188.55 with std. of 34.84174938202731.\n",
      "Episode: 1600\n",
      "The avg. test return for episode 1600 is 185.65 with std. of 24.098288320957572.\n",
      "Episode: 1700\n",
      "The avg. test return for episode 1700 is 183.5 with std. of 34.23813663153998.\n",
      "Episode: 1800\n",
      "The avg. test return for episode 1800 is 198.05 with std. of 8.499852939904315.\n",
      "Episode: 1900\n",
      "The avg. test return for episode 1900 is 126.95 with std. of 36.39708092690951.\n",
      "Episode: 2000\n",
      "The avg. test return for episode 2000 is 200.0 with std. of 0.0.\n",
      "Episode: 2100\n",
      "The avg. test return for episode 2100 is 193.75 with std. of 11.058367872339932.\n",
      "Episode: 2200\n",
      "The avg. test return for episode 2200 is 148.85 with std. of 17.31841505450196.\n",
      "Episode: 2300\n",
      "The avg. test return for episode 2300 is 79.5 with std. of 33.08398404062002.\n",
      "Episode: 2400\n",
      "The avg. test return for episode 2400 is 189.5 with std. of 17.350792489105505.\n",
      "Episode: 2500\n",
      "The avg. test return for episode 2500 is 181.0 with std. of 19.804039991880444.\n",
      "Episode: 2600\n",
      "The avg. test return for episode 2600 is 200.0 with std. of 0.0.\n",
      "Episode: 2700\n",
      "The avg. test return for episode 2700 is 199.95 with std. of 0.2179449471770337.\n",
      "Episode: 2800\n",
      "The avg. test return for episode 2800 is 200.0 with std. of 0.0.\n",
      "Episode: 2900\n",
      "The avg. test return for episode 2900 is 198.35 with std. of 6.142271566773973.\n",
      "Episode: 3000\n",
      "The avg. test return for episode 3000 is 192.2 with std. of 11.96494880891682.\n",
      "Episode: 3100\n",
      "The avg. test return for episode 3100 is 200.0 with std. of 0.0.\n",
      "Episode: 3200\n",
      "The avg. test return for episode 3200 is 200.0 with std. of 0.0.\n",
      "Episode: 3300\n",
      "The avg. test return for episode 3300 is 200.0 with std. of 0.0.\n",
      "Episode: 3400\n",
      "The avg. test return for episode 3400 is 200.0 with std. of 0.0.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 5/5 [24:34<00:00, 294.98s/it]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'REINFORCE Learning Curve')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in tqdm.tqdm(range(num_seeds)):\n",
    "    return_means = []\n",
    "\n",
    "    # Define a policy network\n",
    "    policy_net = NeuralNet(nS, nA, torch.nn.Softmax())\n",
    "    policy_net_optimizer = optim.Adam(policy_net.parameters(), lr=policy_lr)\n",
    "    \n",
    "    for m in range(num_episodes):\n",
    "        # Train a policy network with REINFORCE\n",
    "        train_REINRORCE(env, policy_net, policy_net_optimizer, gamma=gamma)\n",
    "        if m % 100 == 0:\n",
    "            print(f\"Episode: {m}\")\n",
    "            G = np.zeros(20)\n",
    "            for k in range(20): # iterate over 20 test episodes\n",
    "                g = evaluate_policy(env, policy_net)\n",
    "                G[k] = g\n",
    "\n",
    "            return_mean = G.mean()\n",
    "            return_sd = G.std()\n",
    "            print(f\"The avg. test return for episode {m} is {return_mean} with std. of {return_sd}.\")\n",
    "            return_means.append(return_mean)\n",
    "    returns[i] = np.array(return_means)\n",
    "\n",
    "# Plot the performance over iterations\n",
    "ks = np.arange(l)*100\n",
    "avs = np.mean(returns, axis=0)\n",
    "maxs = np.max(returns, axis=0)\n",
    "mins = np.min(returns, axis=0)\n",
    "\n",
    "plt.fill_between(ks, mins, maxs, alpha=0.1)\n",
    "plt.plot(ks, avs, '-o', markersize=1)\n",
    "\n",
    "plt.xlabel('Episode', fontsize = 15)\n",
    "plt.ylabel('Return', fontsize = 15)\n",
    "\n",
    "plt.title(\"REINFORCE Learning Curve\", fontsize = 24)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af8147b5",
   "metadata": {
    "papermill": {
     "duration": 0.034212,
     "end_time": "2023-12-13T16:29:04.264823",
     "exception": false,
     "start_time": "2023-12-13T16:29:04.230611",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "In the above plot, the line shows the average return over 5 seeds and the shading shows the range between the min and max of returns for 5 seeds.\n",
    "\n",
    "The learned policy does not achieve the maximum return (200) on average within 3500 episodes and there are large performance variances (i.e. the performance is unstable). But we can see that the policy gets better by having more episodes with REINFORCE."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2de002d",
   "metadata": {
    "papermill": {
     "duration": 0.035158,
     "end_time": "2023-12-13T16:29:04.334981",
     "exception": false,
     "start_time": "2023-12-13T16:29:04.299823",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## REINFORCE with baseline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ebb9c4c0",
   "metadata": {
    "papermill": {
     "duration": 0.035095,
     "end_time": "2023-12-13T16:29:04.405570",
     "exception": false,
     "start_time": "2023-12-13T16:29:04.370475",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "One problem of REINFORCE is its high variance and thus produces slow learning. The REINFORCE algorithm estimates the gradient of the objective function using the expected returns by sampling trajectories. Because it relies on sampled trajectories, the gradient estimates can have high variance, leading to noisy updates. This high variance can result in large fluctuations in the policy parameters during training.\n",
    "\n",
    "One idea to reduce this fluctuation is to include a comparison of the value to an arbitrary baseline $b(S_t)$:\n",
    "\\begin{align*}\n",
    "\\theta_{t+1} &= \\theta_t + \\alpha G_t \\nabla \\ln \\pi(A_t|S_t,\\theta) \\quad (\\text{REINFORCE})\\\\\n",
    "\\\\\n",
    "\\theta_{t+1} &= \\theta_t + \\alpha (G_t-b(S_t)) \\nabla \\ln \\pi(A_t|S_t,\\theta) \\quad (\\text{REINFORCE with baseline})\n",
    "\\end{align*}\n",
    "\n",
    "$(G_t-b(S_t))$ term is called advantage. The advantage represents how much better or worse the return by the current action is compared to the expected return at the state $S_t$. The baseline effectively reduces the scale of the return term in the policy gradient update. Since the advantage is multiplied by the gradient of the log probability of the action, a smaller advantage term results in smaller updates to the policy, leading to more stable policy gradient updates.\n",
    "\n",
    "But is this a valid operation? In other words, even after subtracting the baseline, can the above equation be utilized as the estimate of the gradient of the objective function $J(\\theta)$? We can show that this is a valid operation because adding the baseline term does not actually change the value of the equation as follows:\n",
    "\n",
    "\\begin{align*}\n",
    "&\\sum_s \\mu(s) \\sum_a (q_{\\pi}(s,a)-b(s)) \\nabla \\pi(a|s, \\theta) \\\\\n",
    "&= \\sum_s \\mu(s) \\sum_a (q_{\\pi}(s,a)) \\nabla \\pi(a|s, \\theta)-\\sum_s \\mu(s) \\sum_a (b(s)) \\nabla \\pi(a|s, \\theta) \\\\\n",
    "&= \\sum_s \\mu(s) \\sum_a (q_{\\pi}(s,a)) \\nabla \\pi(a|s, \\theta)-\\sum_s \\mu(s)  (b(s)) \\nabla \\sum_a \\pi(a|s, \\theta) \\\\\n",
    "&= \\sum_s \\mu(s) \\sum_a (q_{\\pi}(s,a)) \\nabla \\pi(a|s, \\theta)-\\sum_s \\mu(s)  (b(s)) \\nabla 1 \\quad (\\text{because } \\sum_a \\pi(a|s, \\theta)=1) \\\\\n",
    "&= \\sum_s \\mu(s) \\sum_a q_{\\pi}(s,a) \\nabla \\pi(a|s, \\theta) \\quad (\\text{because } \\nabla 1=0) \\\\\n",
    "&\\propto \\nabla J(\\theta)\n",
    "\\end{align*}\n",
    "\n",
    "The baseline can be any function, as long as it does not vary with $a$ because the gradient update equation remains valid/same even with adding $b(s)$. For example, we can use a constant value as a baseline for all states or some kind of regression model to estimate the average value at each state $s$.\n",
    "\n",
    "When the baseline is uniformly zero, this update is the same as REINFORCE. Thus, this REINFORCE with baseline is a generalization of REINFORCE (or in other words, REINFORCE is a special case of REINFORCE with baseline).\n",
    "\n",
    "Below is the pseudo-code of this update. In the below pseudo-code, the baseline state value is estimated by a parametric model with parameter $w$. \n"
   ]
  },
  {
   "attachments": {
    "image-2.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "a0db501d",
   "metadata": {
    "papermill": {
     "duration": 0.034294,
     "end_time": "2023-12-13T16:29:04.475409",
     "exception": false,
     "start_time": "2023-12-13T16:29:04.441115",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "![image-2.png](attachment:image-2.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ccb6131",
   "metadata": {
    "papermill": {
     "duration": 0.035864,
     "end_time": "2023-12-13T16:29:04.546528",
     "exception": false,
     "start_time": "2023-12-13T16:29:04.510664",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "In the above pseudo-code, while we update the parameter for policy network $\\theta$, we also update the parameter for the state value prediction model $w$ by using the advantage. The state value estimate parameter update uses the mean squared loss to minimize the prediction error between the predicted baseline value function and observed return. \n",
    "Note that in this algorithm, we have two different learning rates for each parameter, $\\alpha^{\\theta}$ and $\\alpha^{w}$, which are hyperparameters of this algorithm.\n",
    "\n",
    "The below code shows the implementation of the train function for REINFORCE + baseline."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "124f4d28",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-12-13T16:29:04.618561Z",
     "iopub.status.busy": "2023-12-13T16:29:04.618097Z",
     "iopub.status.idle": "2023-12-13T16:29:04.628164Z",
     "shell.execute_reply": "2023-12-13T16:29:04.626976Z"
    },
    "papermill": {
     "duration": 0.048393,
     "end_time": "2023-12-13T16:29:04.630352",
     "exception": false,
     "start_time": "2023-12-13T16:29:04.581959",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "def train_REINRORCE_baseline(env, policy_net, policy_optimizer, value_net, value_optimizer, gamma=0.99):\n",
    "    \"\"\"\n",
    "    Trains the policy network on a single episode using REINFORCE with baseline\n",
    "    \"\"\"\n",
    "\n",
    "    # Generate an episode with the current policy network\n",
    "    states, actions, rewards, log_probs = generate_episode(env, policy_net)\n",
    "    T = len(states)\n",
    "    \n",
    "    # Create tensors\n",
    "    states = np.vstack(states).astype(float)\n",
    "    states = torch.FloatTensor(states).to(device)\n",
    "    actions = torch.LongTensor(actions).to(device).view(-1,1)\n",
    "    rewards = torch.FloatTensor(rewards).to(device).view(-1,1)\n",
    "\n",
    "    # Compute total discounted return at each time step\n",
    "    Gs = []\n",
    "    G = 0\n",
    "    for t in range(T-1,-1,-1): # iterate in backward order to make the computation easier\n",
    "        G = rewards[t] + gamma*G\n",
    "        Gs.insert(0,G)\n",
    "    Gs = torch.tensor(Gs).view(-1,1)\n",
    "    \n",
    "    # Compute the advantage\n",
    "    state_vals = value_net(states).to(device)\n",
    "    with torch.no_grad():\n",
    "        advantages = Gs - state_vals\n",
    "        \n",
    "    # Update policy network weights\n",
    "    L_theta = torch.stack([-log_prob * advantage for log_prob, advantage in zip(log_probs, advantages)]).sum() / T\n",
    "    policy_optimizer.zero_grad()\n",
    "    L_theta.backward()\n",
    "    policy_optimizer.step() \n",
    "    \n",
    "    # Update value network weights\n",
    "    loss_fn = nn.MSELoss()\n",
    "    value_loss = loss_fn(state_vals, Gs)\n",
    "    value_optimizer.zero_grad()\n",
    "    value_loss.backward()\n",
    "    value_optimizer.step() \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31ad12af",
   "metadata": {
    "papermill": {
     "duration": 0.034629,
     "end_time": "2023-12-13T16:29:04.699729",
     "exception": false,
     "start_time": "2023-12-13T16:29:04.665100",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "Let's test whether REINFORCE with baseline can learn a good policy and reduce the variance in learning. \n",
    "As we did for REINFORCE, in the below code, we train the policy network for 3,500 episodes using 5 different random seeds. We freeze the weights of the network every 100 episodes and perform 20 episodes with the current policy to evaluate the test performance of the policy at each training phase. \n",
    "\n",
    "Note: The below code may take about 10 min to run."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "04e3db7b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-12-13T16:29:04.771663Z",
     "iopub.status.busy": "2023-12-13T16:29:04.770471Z",
     "iopub.status.idle": "2023-12-13T17:02:07.650902Z",
     "shell.execute_reply": "2023-12-13T17:02:07.649779Z"
    },
    "papermill": {
     "duration": 1982.918695,
     "end_time": "2023-12-13T17:02:07.653212",
     "exception": false,
     "start_time": "2023-12-13T16:29:04.734517",
     "status": "completed"
    },
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/5 [00:00<?, ?it/s]/tmp/ipykernel_19/332058975.py:27: UserWarning: Implicit dimension choice for softmax has been deprecated. Change the call to include dim=X as an argument.\n",
      "  x = self.output_activation(self.output_layer(x))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode: 0\n",
      "The avg. test reward for episode 0 is 20.85 with std of 9.650259063880098.\n",
      "Episode: 100\n",
      "The avg. test reward for episode 100 is 20.4 with std of 9.66126285741155.\n",
      "Episode: 200\n",
      "The avg. test reward for episode 200 is 26.4 with std of 16.532997308413258.\n",
      "Episode: 300\n",
      "The avg. test reward for episode 300 is 26.15 with std of 13.569358864736389.\n",
      "Episode: 400\n",
      "The avg. test reward for episode 400 is 56.45 with std of 24.152587853064524.\n",
      "Episode: 500\n",
      "The avg. test reward for episode 500 is 164.6 with std of 33.62350368417901.\n",
      "Episode: 600\n",
      "The avg. test reward for episode 600 is 197.95 with std of 8.935742834258381.\n",
      "Episode: 700\n",
      "The avg. test reward for episode 700 is 196.1 with std of 16.999705879808626.\n",
      "Episode: 800\n",
      "The avg. test reward for episode 800 is 197.0 with std of 13.076696830622021.\n",
      "Episode: 900\n",
      "The avg. test reward for episode 900 is 195.2 with std of 16.740967713964448.\n",
      "Episode: 1000\n",
      "The avg. test reward for episode 1000 is 197.1 with std of 10.944861808172819.\n",
      "Episode: 1100\n",
      "The avg. test reward for episode 1100 is 195.1 with std of 18.592740518815404.\n",
      "Episode: 1200\n",
      "The avg. test reward for episode 1200 is 200.0 with std of 0.0.\n",
      "Episode: 1300\n",
      "The avg. test reward for episode 1300 is 199.8 with std of 0.8717797887081347.\n",
      "Episode: 1400\n",
      "The avg. test reward for episode 1400 is 195.95 with std of 8.890866099542835.\n",
      "Episode: 1500\n",
      "The avg. test reward for episode 1500 is 198.45 with std of 4.96462485994662.\n",
      "Episode: 1600\n",
      "The avg. test reward for episode 1600 is 199.0 with std of 4.358898943540674.\n",
      "Episode: 1700\n",
      "The avg. test reward for episode 1700 is 185.55 with std of 40.8698850010616.\n",
      "Episode: 1800\n",
      "The avg. test reward for episode 1800 is 200.0 with std of 0.0.\n",
      "Episode: 1900\n",
      "The avg. test reward for episode 1900 is 200.0 with std of 0.0.\n",
      "Episode: 2000\n",
      "The avg. test reward for episode 2000 is 196.7 with std of 14.384366513684224.\n",
      "Episode: 2100\n",
      "The avg. test reward for episode 2100 is 184.85 with std of 16.74895519129477.\n",
      "Episode: 2200\n",
      "The avg. test reward for episode 2200 is 199.05 with std of 4.14095399636364.\n",
      "Episode: 2300\n",
      "The avg. test reward for episode 2300 is 200.0 with std of 0.0.\n",
      "Episode: 2400\n",
      "The avg. test reward for episode 2400 is 188.0 with std of 13.337915879176926.\n",
      "Episode: 2500\n",
      "The avg. test reward for episode 2500 is 200.0 with std of 0.0.\n",
      "Episode: 2600\n",
      "The avg. test reward for episode 2600 is 200.0 with std of 0.0.\n",
      "Episode: 2700\n",
      "The avg. test reward for episode 2700 is 200.0 with std of 0.0.\n",
      "Episode: 2800\n",
      "The avg. test reward for episode 2800 is 198.7 with std of 5.666568626602875.\n",
      "Episode: 2900\n",
      "The avg. test reward for episode 2900 is 199.55 with std of 1.9615045245933032.\n",
      "Episode: 3000\n",
      "The avg. test reward for episode 3000 is 200.0 with std of 0.0.\n",
      "Episode: 3100\n",
      "The avg. test reward for episode 3100 is 200.0 with std of 0.0.\n",
      "Episode: 3200\n",
      "The avg. test reward for episode 3200 is 197.1 with std of 12.640806936267952.\n",
      "Episode: 3300\n",
      "The avg. test reward for episode 3300 is 197.15 with std of 12.422861989090919.\n",
      "Episode: 3400\n",
      "The avg. test reward for episode 3400 is 199.35 with std of 2.833284313301438.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 20%|██        | 1/5 [06:56<27:47, 416.96s/it]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode: 0\n",
      "The avg. test reward for episode 0 is 24.15 with std of 10.82254591119853.\n",
      "Episode: 100\n",
      "The avg. test reward for episode 100 is 21.25 with std of 8.049068269060712.\n",
      "Episode: 200\n",
      "The avg. test reward for episode 200 is 33.45 with std of 19.371306099486425.\n",
      "Episode: 300\n",
      "The avg. test reward for episode 300 is 65.0 with std of 32.66802718255267.\n",
      "Episode: 400\n",
      "The avg. test reward for episode 400 is 153.1 with std of 50.09880238089529.\n",
      "Episode: 500\n",
      "The avg. test reward for episode 500 is 143.2 with std of 39.5797928241167.\n",
      "Episode: 600\n",
      "The avg. test reward for episode 600 is 183.55 with std of 28.098887878348492.\n",
      "Episode: 700\n",
      "The avg. test reward for episode 700 is 196.0 with std of 9.044335243676011.\n",
      "Episode: 800\n",
      "The avg. test reward for episode 800 is 199.25 with std of 2.021756661915573.\n",
      "Episode: 900\n",
      "The avg. test reward for episode 900 is 195.75 with std of 11.682786482684685.\n",
      "Episode: 1000\n",
      "The avg. test reward for episode 1000 is 196.0 with std of 10.094552986635911.\n",
      "Episode: 1100\n",
      "The avg. test reward for episode 1100 is 199.05 with std of 2.2907422377910613.\n",
      "Episode: 1200\n",
      "The avg. test reward for episode 1200 is 196.45 with std of 7.290233192429445.\n",
      "Episode: 1300\n",
      "The avg. test reward for episode 1300 is 191.55 with std of 12.623291963667796.\n",
      "Episode: 1400\n",
      "The avg. test reward for episode 1400 is 200.0 with std of 0.0.\n",
      "Episode: 1500\n",
      "The avg. test reward for episode 1500 is 200.0 with std of 0.0.\n",
      "Episode: 1600\n",
      "The avg. test reward for episode 1600 is 200.0 with std of 0.0.\n",
      "Episode: 1700\n",
      "The avg. test reward for episode 1700 is 181.25 with std of 25.473270304379845.\n",
      "Episode: 1800\n",
      "The avg. test reward for episode 1800 is 200.0 with std of 0.0.\n",
      "Episode: 1900\n",
      "The avg. test reward for episode 1900 is 200.0 with std of 0.0.\n",
      "Episode: 2000\n",
      "The avg. test reward for episode 2000 is 198.85 with std of 5.012733785071774.\n",
      "Episode: 2100\n",
      "The avg. test reward for episode 2100 is 191.8 with std of 35.74297133703353.\n",
      "Episode: 2200\n",
      "The avg. test reward for episode 2200 is 200.0 with std of 0.0.\n",
      "Episode: 2300\n",
      "The avg. test reward for episode 2300 is 195.0 with std of 10.963576058932597.\n",
      "Episode: 2400\n",
      "The avg. test reward for episode 2400 is 200.0 with std of 0.0.\n",
      "Episode: 2500\n",
      "The avg. test reward for episode 2500 is 200.0 with std of 0.0.\n",
      "Episode: 2600\n",
      "The avg. test reward for episode 2600 is 200.0 with std of 0.0.\n",
      "Episode: 2700\n",
      "The avg. test reward for episode 2700 is 200.0 with std of 0.0.\n",
      "Episode: 2800\n",
      "The avg. test reward for episode 2800 is 200.0 with std of 0.0.\n",
      "Episode: 2900\n",
      "The avg. test reward for episode 2900 is 185.15 with std of 23.371510434715166.\n",
      "Episode: 3000\n",
      "The avg. test reward for episode 3000 is 195.55 with std of 11.867918941415128.\n",
      "Episode: 3100\n",
      "The avg. test reward for episode 3100 is 195.85 with std of 7.7412854229772465.\n",
      "Episode: 3200\n",
      "The avg. test reward for episode 3200 is 200.0 with std of 0.0.\n",
      "Episode: 3300\n",
      "The avg. test reward for episode 3300 is 198.5 with std of 3.626292872893749.\n",
      "Episode: 3400\n",
      "The avg. test reward for episode 3400 is 200.0 with std of 0.0.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 40%|████      | 2/5 [13:50<20:45, 415.20s/it]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode: 0\n",
      "The avg. test reward for episode 0 is 18.5 with std of 7.870832230456955.\n",
      "Episode: 100\n",
      "The avg. test reward for episode 100 is 19.95 with std of 9.962303950392197.\n",
      "Episode: 200\n",
      "The avg. test reward for episode 200 is 33.45 with std of 17.791781810712497.\n",
      "Episode: 300\n",
      "The avg. test reward for episode 300 is 38.25 with std of 21.80796872705021.\n",
      "Episode: 400\n",
      "The avg. test reward for episode 400 is 59.1 with std of 36.9904041610794.\n",
      "Episode: 500\n",
      "The avg. test reward for episode 500 is 105.65 with std of 43.9753055702857.\n",
      "Episode: 600\n",
      "The avg. test reward for episode 600 is 137.8 with std of 33.3970058538187.\n",
      "Episode: 700\n",
      "The avg. test reward for episode 700 is 185.2 with std of 21.40700819825134.\n",
      "Episode: 800\n",
      "The avg. test reward for episode 800 is 186.6 with std of 37.53851355607997.\n",
      "Episode: 900\n",
      "The avg. test reward for episode 900 is 200.0 with std of 0.0.\n",
      "Episode: 1000\n",
      "The avg. test reward for episode 1000 is 200.0 with std of 0.0.\n",
      "Episode: 1100\n",
      "The avg. test reward for episode 1100 is 195.75 with std of 12.513492717862588.\n",
      "Episode: 1200\n",
      "The avg. test reward for episode 1200 is 200.0 with std of 0.0.\n",
      "Episode: 1300\n",
      "The avg. test reward for episode 1300 is 200.0 with std of 0.0.\n",
      "Episode: 1400\n",
      "The avg. test reward for episode 1400 is 186.25 with std of 31.19435045004143.\n",
      "Episode: 1500\n",
      "The avg. test reward for episode 1500 is 197.4 with std of 11.33313725320575.\n",
      "Episode: 1600\n",
      "The avg. test reward for episode 1600 is 195.25 with std of 20.7047699818182.\n",
      "Episode: 1700\n",
      "The avg. test reward for episode 1700 is 200.0 with std of 0.0.\n",
      "Episode: 1800\n",
      "The avg. test reward for episode 1800 is 200.0 with std of 0.0.\n",
      "Episode: 1900\n",
      "The avg. test reward for episode 1900 is 182.2 with std of 34.92076746006593.\n",
      "Episode: 2000\n",
      "The avg. test reward for episode 2000 is 190.75 with std of 28.07645810995397.\n",
      "Episode: 2100\n",
      "The avg. test reward for episode 2100 is 200.0 with std of 0.0.\n",
      "Episode: 2200\n",
      "The avg. test reward for episode 2200 is 200.0 with std of 0.0.\n",
      "Episode: 2300\n",
      "The avg. test reward for episode 2300 is 200.0 with std of 0.0.\n",
      "Episode: 2400\n",
      "The avg. test reward for episode 2400 is 200.0 with std of 0.0.\n",
      "Episode: 2500\n",
      "The avg. test reward for episode 2500 is 184.25 with std of 32.02011086801543.\n",
      "Episode: 2600\n",
      "The avg. test reward for episode 2600 is 197.6 with std of 6.319810123729984.\n",
      "Episode: 2700\n",
      "The avg. test reward for episode 2700 is 198.4 with std of 5.580322571321482.\n",
      "Episode: 2800\n",
      "The avg. test reward for episode 2800 is 200.0 with std of 0.0.\n",
      "Episode: 2900\n",
      "The avg. test reward for episode 2900 is 197.8 with std of 9.589577675789482.\n",
      "Episode: 3000\n",
      "The avg. test reward for episode 3000 is 198.55 with std of 6.320403468133977.\n",
      "Episode: 3100\n",
      "The avg. test reward for episode 3100 is 199.3 with std of 3.0512292604784714.\n",
      "Episode: 3200\n",
      "The avg. test reward for episode 3200 is 200.0 with std of 0.0.\n",
      "Episode: 3300\n",
      "The avg. test reward for episode 3300 is 200.0 with std of 0.0.\n",
      "Episode: 3400\n",
      "The avg. test reward for episode 3400 is 200.0 with std of 0.0.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 60%|██████    | 3/5 [20:27<13:33, 406.90s/it]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode: 0\n",
      "The avg. test reward for episode 0 is 21.4 with std of 10.204900783447139.\n",
      "Episode: 100\n",
      "The avg. test reward for episode 100 is 20.15 with std of 11.03754954688766.\n",
      "Episode: 200\n",
      "The avg. test reward for episode 200 is 28.6 with std of 31.060264004029335.\n",
      "Episode: 300\n",
      "The avg. test reward for episode 300 is 37.0 with std of 18.62256695517565.\n",
      "Episode: 400\n",
      "The avg. test reward for episode 400 is 69.75 with std of 30.629846555280032.\n",
      "Episode: 500\n",
      "The avg. test reward for episode 500 is 163.3 with std of 46.19859305216989.\n",
      "Episode: 600\n",
      "The avg. test reward for episode 600 is 132.45 with std of 51.693785893470796.\n",
      "Episode: 700\n",
      "The avg. test reward for episode 700 is 180.05 with std of 26.121782098470998.\n",
      "Episode: 800\n",
      "The avg. test reward for episode 800 is 190.2 with std of 30.878147612834557.\n",
      "Episode: 900\n",
      "The avg. test reward for episode 900 is 192.2 with std of 33.99941175961725.\n",
      "Episode: 1000\n",
      "The avg. test reward for episode 1000 is 200.0 with std of 0.0.\n",
      "Episode: 1100\n",
      "The avg. test reward for episode 1100 is 194.7 with std of 10.8816359064251.\n",
      "Episode: 1200\n",
      "The avg. test reward for episode 1200 is 200.0 with std of 0.0.\n",
      "Episode: 1300\n",
      "The avg. test reward for episode 1300 is 191.1 with std of 15.029637387508723.\n",
      "Episode: 1400\n",
      "The avg. test reward for episode 1400 is 195.55 with std of 9.769723639898931.\n",
      "Episode: 1500\n",
      "The avg. test reward for episode 1500 is 198.9 with std of 4.357751713900185.\n",
      "Episode: 1600\n",
      "The avg. test reward for episode 1600 is 200.0 with std of 0.0.\n",
      "Episode: 1700\n",
      "The avg. test reward for episode 1700 is 200.0 with std of 0.0.\n",
      "Episode: 1800\n",
      "The avg. test reward for episode 1800 is 200.0 with std of 0.0.\n",
      "Episode: 1900\n",
      "The avg. test reward for episode 1900 is 199.0 with std of 3.0166206257996713.\n",
      "Episode: 2000\n",
      "The avg. test reward for episode 2000 is 200.0 with std of 0.0.\n",
      "Episode: 2100\n",
      "The avg. test reward for episode 2100 is 200.0 with std of 0.0.\n",
      "Episode: 2200\n",
      "The avg. test reward for episode 2200 is 199.85 with std of 0.6538348415311008.\n",
      "Episode: 2300\n",
      "The avg. test reward for episode 2300 is 199.4 with std of 2.6153393661244038.\n",
      "Episode: 2400\n",
      "The avg. test reward for episode 2400 is 199.5 with std of 1.4317821063276353.\n",
      "Episode: 2500\n",
      "The avg. test reward for episode 2500 is 200.0 with std of 0.0.\n",
      "Episode: 2600\n",
      "The avg. test reward for episode 2600 is 200.0 with std of 0.0.\n",
      "Episode: 2700\n",
      "The avg. test reward for episode 2700 is 196.95 with std of 5.920092904676413.\n",
      "Episode: 2800\n",
      "The avg. test reward for episode 2800 is 200.0 with std of 0.0.\n",
      "Episode: 2900\n",
      "The avg. test reward for episode 2900 is 200.0 with std of 0.0.\n",
      "Episode: 3000\n",
      "The avg. test reward for episode 3000 is 200.0 with std of 0.0.\n",
      "Episode: 3100\n",
      "The avg. test reward for episode 3100 is 194.2 with std of 7.586830695356263.\n",
      "Episode: 3200\n",
      "The avg. test reward for episode 3200 is 197.0 with std of 5.059644256269407.\n",
      "Episode: 3300\n",
      "The avg. test reward for episode 3300 is 200.0 with std of 0.0.\n",
      "Episode: 3400\n",
      "The avg. test reward for episode 3400 is 200.0 with std of 0.0.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 80%|████████  | 4/5 [27:09<06:44, 404.80s/it]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode: 0\n",
      "The avg. test reward for episode 0 is 17.8 with std of 6.297618597533515.\n",
      "Episode: 100\n",
      "The avg. test reward for episode 100 is 19.65 with std of 5.8247317534801555.\n",
      "Episode: 200\n",
      "The avg. test reward for episode 200 is 25.15 with std of 10.887033572098508.\n",
      "Episode: 300\n",
      "The avg. test reward for episode 300 is 27.75 with std of 13.018736497832654.\n",
      "Episode: 400\n",
      "The avg. test reward for episode 400 is 31.25 with std of 16.099301227071937.\n",
      "Episode: 500\n",
      "The avg. test reward for episode 500 is 32.25 with std of 20.39822296181704.\n",
      "Episode: 600\n",
      "The avg. test reward for episode 600 is 32.35 with std of 15.726649357062678.\n",
      "Episode: 700\n",
      "The avg. test reward for episode 700 is 48.05 with std of 43.02263938904725.\n",
      "Episode: 800\n",
      "The avg. test reward for episode 800 is 82.8 with std of 45.37576445637032.\n",
      "Episode: 900\n",
      "The avg. test reward for episode 900 is 139.1 with std of 60.20041528095965.\n",
      "Episode: 1000\n",
      "The avg. test reward for episode 1000 is 170.95 with std of 38.995480507361364.\n",
      "Episode: 1100\n",
      "The avg. test reward for episode 1100 is 184.4 with std of 26.71591286106466.\n",
      "Episode: 1200\n",
      "The avg. test reward for episode 1200 is 196.0 with std of 14.173919711921611.\n",
      "Episode: 1300\n",
      "The avg. test reward for episode 1300 is 200.0 with std of 0.0.\n",
      "Episode: 1400\n",
      "The avg. test reward for episode 1400 is 200.0 with std of 0.0.\n",
      "Episode: 1500\n",
      "The avg. test reward for episode 1500 is 200.0 with std of 0.0.\n",
      "Episode: 1600\n",
      "The avg. test reward for episode 1600 is 177.1 with std of 27.732471941750884.\n",
      "Episode: 1700\n",
      "The avg. test reward for episode 1700 is 200.0 with std of 0.0.\n",
      "Episode: 1800\n",
      "The avg. test reward for episode 1800 is 198.1 with std of 5.734980383575867.\n",
      "Episode: 1900\n",
      "The avg. test reward for episode 1900 is 186.5 with std of 19.464069461446133.\n",
      "Episode: 2000\n",
      "The avg. test reward for episode 2000 is 199.85 with std of 0.6538348415311008.\n",
      "Episode: 2100\n",
      "The avg. test reward for episode 2100 is 200.0 with std of 0.0.\n",
      "Episode: 2200\n",
      "The avg. test reward for episode 2200 is 200.0 with std of 0.0.\n",
      "Episode: 2300\n",
      "The avg. test reward for episode 2300 is 200.0 with std of 0.0.\n",
      "Episode: 2400\n",
      "The avg. test reward for episode 2400 is 195.15 with std of 13.569358864736389.\n",
      "Episode: 2500\n",
      "The avg. test reward for episode 2500 is 198.7 with std of 5.666568626602875.\n",
      "Episode: 2600\n",
      "The avg. test reward for episode 2600 is 200.0 with std of 0.0.\n",
      "Episode: 2700\n",
      "The avg. test reward for episode 2700 is 194.25 with std of 12.703838002745469.\n",
      "Episode: 2800\n",
      "The avg. test reward for episode 2800 is 200.0 with std of 0.0.\n",
      "Episode: 2900\n",
      "The avg. test reward for episode 2900 is 200.0 with std of 0.0.\n",
      "Episode: 3000\n",
      "The avg. test reward for episode 3000 is 197.15 with std of 12.42286198909092.\n",
      "Episode: 3100\n",
      "The avg. test reward for episode 3100 is 198.35 with std of 7.192183256842112.\n",
      "Episode: 3200\n",
      "The avg. test reward for episode 3200 is 200.0 with std of 0.0.\n",
      "Episode: 3300\n",
      "The avg. test reward for episode 3300 is 195.15 with std of 21.140659876172265.\n",
      "Episode: 3400\n",
      "The avg. test reward for episode 3400 is 200.0 with std of 0.0.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 5/5 [33:02<00:00, 396.51s/it]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'REINFORCE with baseline Learning Curve')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "policy_lr = 5e-4\n",
    "baseline_lr = 5e-4\n",
    "returns = np.zeros((num_seeds, l)) # dim: (5 ,35)\n",
    "\n",
    "for i in tqdm.tqdm(range(num_seeds)):\n",
    "    reward_means = []\n",
    "\n",
    "    # Define policy and value networks\n",
    "    policy_net = NeuralNet(nS, nA, torch.nn.Softmax())\n",
    "    policy_net_optimizer = optim.Adam(policy_net.parameters(), lr=policy_lr)\n",
    "    value_net = NeuralNet(nS, 1, torch.nn.ReLU())\n",
    "    value_net_optimizer = optim.Adam(value_net.parameters(), lr=baseline_lr)\n",
    "    \n",
    "    for m in range(num_episodes):\n",
    "        # Train networks with REINFORCE with baseline\n",
    "        train_REINRORCE_baseline(env, policy_net, policy_net_optimizer, value_net, value_net_optimizer, gamma=gamma)\n",
    "        if m % 100 == 0:\n",
    "            print(\"Episode: {}\".format(m))\n",
    "            G = np.zeros(20)\n",
    "            for k in range(20):\n",
    "                g = evaluate_policy(env, policy_net)\n",
    "                G[k] = g\n",
    "\n",
    "            reward_mean = G.mean()\n",
    "            reward_sd = G.std()\n",
    "            print(\"The avg. test reward for episode {0} is {1} with std of {2}.\".format(m, reward_mean, reward_sd))\n",
    "            reward_means.append(reward_mean)\n",
    "    returns[i] = np.array(reward_means)\n",
    "\n",
    "    \n",
    "# Plot the performance over iterations\n",
    "ks = np.arange(l)*100\n",
    "avs = np.mean(returns, axis=0)\n",
    "maxs = np.max(returns, axis=0)\n",
    "mins = np.min(returns, axis=0)\n",
    "\n",
    "plt.fill_between(ks, mins, maxs, alpha=0.1)\n",
    "plt.plot(ks, avs, '-o', markersize=1)\n",
    "\n",
    "plt.xlabel('Episode', fontsize = 15)\n",
    "plt.ylabel('Return', fontsize = 15)\n",
    "\n",
    "plt.title(\"REINFORCE with baseline Learning Curve\", fontsize = 24)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd4e18ed",
   "metadata": {
    "papermill": {
     "duration": 0.0565,
     "end_time": "2023-12-13T17:02:07.766345",
     "exception": false,
     "start_time": "2023-12-13T17:02:07.709845",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "REINFORCE with baseline converges to the best performance around 1000th episodes (although the result could slightly vary on each run) and achieves a much smaller variance compared to REINFORCE as we expected. The use of a baseline offered a significant performance improvement in this case."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ed02821e",
   "metadata": {
    "papermill": {
     "duration": 0.056965,
     "end_time": "2023-12-13T17:02:07.880581",
     "exception": false,
     "start_time": "2023-12-13T17:02:07.823616",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Actor Critic"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2af4f888",
   "metadata": {
    "papermill": {
     "duration": 0.056623,
     "end_time": "2023-12-13T17:02:07.993718",
     "exception": false,
     "start_time": "2023-12-13T17:02:07.937095",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "One disadvantage of REINFORCE and REINFORCE+baseline is that it has to wait until the end of the episode to perform the update because the update depends on the return $G$. Another disadvantage is while introducing baseline relieves the large variance, the variance often remains high because the algorithm relies on the noisy sampled return $G$. \n",
    "These disadvantages are similar to Monte Carlo Methods for solving finite Markov Decision Process (MDP). To overcome this limitation, in the MDP setup, we use TD-learning, which uses value estimate to perform the online update of the estimate (i.e. bootstrapping). This helps reduce the variance too by removing the dependency on the sampled return $G$.\n",
    "\n",
    "Can we use a similar strategy in the case of policy gradient? Yes, we can. Let's think about how we can replace return term $G$ in the REINFORCE with baseline update equation with a value estimate. The simplest thing we can do is to estimate the state value as the sum of the immediate reward and the value of the next state, i.e. $R_{t+1}+\\gamma \\widehat{v}(S_{t+1}, w)$ as we do with TD(0) method (You can learn more about TD(0) in [this notebook](https://www.kaggle.com/code/minaiyuki/solving-mdp-using-td-learning-sarsa-q-learning)). Then, we can write down the policy parameter update equation with advantage as follows:\n",
    "\n",
    "$$\\theta_{t+1}=\\theta_t + \\alpha (R_{t+1}+\\gamma \\widehat{v}(S_{t+1}, w)-\\widehat{v}(S_t, w)) \\nabla \\ln \\pi(A_t|S_t,\\theta)$$\n",
    "\n",
    "This algorithm using the sum of immediate reward and the value estimate of the next state is called a one-step acrot-critic method. \n",
    "\n",
    "In general. methods that learn approximations to both policy and value functions are called actor-critic methods, where the actor refers to the learned policy, and the critic refers to the learned value function.\n",
    "\n",
    "Below is the pseudo-code of the N-step Actor-Critic algorithm, which is a generalization of the one-step actor critic method and uses the sum of the N-step of immediate return and state value estimate of the next state.\n"
   ]
  },
  {
   "attachments": {
    "image-4.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "e139cea8",
   "metadata": {
    "papermill": {
     "duration": 0.056386,
     "end_time": "2023-12-13T17:02:08.106594",
     "exception": false,
     "start_time": "2023-12-13T17:02:08.050208",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "![image-4.png](attachment:image-4.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e9fe7f76",
   "metadata": {
    "papermill": {
     "duration": 0.056028,
     "end_time": "2023-12-13T17:02:08.220051",
     "exception": false,
     "start_time": "2023-12-13T17:02:08.164023",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "We can see that the return term ($G_t$) uses the value estimate while we did not have this term in REINFORCE+baseline.\n",
    "$$ G_t = \\sum^T_{k=t+1}\\gamma^{k-t-1}R_k  \\quad (\\text{REINFORCE with baseline})$$\n",
    "$$ G_t = (\\sum^{\\min(t+N, T)}_{k=t+1}\\gamma^{k-t-1}R_k)+\\gamma^N V_{end}  \\quad (\\text{Actor Critic})$$\n",
    "\n",
    "Let's see the implementation of this N-step Actor-Critic method.\n",
    "\n",
    "Note: The below code may take about 10 min to run."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "b17f9d90",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-12-13T17:02:08.337435Z",
     "iopub.status.busy": "2023-12-13T17:02:08.337043Z",
     "iopub.status.idle": "2023-12-13T17:02:08.348252Z",
     "shell.execute_reply": "2023-12-13T17:02:08.347026Z"
    },
    "papermill": {
     "duration": 0.073356,
     "end_time": "2023-12-13T17:02:08.350701",
     "exception": false,
     "start_time": "2023-12-13T17:02:08.277345",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Implementation\n",
    "def train_actor_critic(env, policy_net, policy_optimizer, value_net, value_optimizer, gamma=0.99):\n",
    "    \"\"\"\n",
    "    Trains the policy network on a single episode using Actor Critic\n",
    "    \"\"\"\n",
    "\n",
    "    # Generate an episode with the current policy network\n",
    "    states, actions, rewards, log_probs = generate_episode(env, policy_net)\n",
    "    T = len(states)\n",
    "    \n",
    "    # Create tensors\n",
    "    states = np.vstack(states).astype(float)\n",
    "    states = torch.FloatTensor(states).to(device)\n",
    "    actions = torch.LongTensor(actions).to(device).view(-1,1)\n",
    "    rewards = torch.FloatTensor(rewards).to(device).view(-1,1)\n",
    "    # log_probs = torch.FloatTensor(log_probs).to(device).view(-1,1)\n",
    "\n",
    "    # Initialize Gs as an empty list\n",
    "    Gs = []\n",
    "\n",
    "    # Loop through each time step\n",
    "    for t in range(T):\n",
    "        end_time = t + n if t + n < T else T  # Determine the end of the trajectory\n",
    "\n",
    "        # Calculate the discounted return G for time step t\n",
    "        G = 0\n",
    "        for t_inner in range(t, end_time):\n",
    "            G += gamma**(t_inner - t) * rewards[t_inner]\n",
    "            \n",
    "        # If end_time is within the trajectory, add the value function estimate\n",
    "        if end_time < T:\n",
    "            V_end = value_net.forward(states[end_time]).item()\n",
    "            G += gamma**n * V_end\n",
    "\n",
    "        # Append the calculated G to the list\n",
    "        Gs.append(G)\n",
    "        \n",
    "    Gs = torch.tensor(Gs).view(-1,1)\n",
    "\n",
    "    # Compute the advantage\n",
    "    state_vals = value_net(states).to(device)\n",
    "    with torch.no_grad():\n",
    "        advantages = Gs - state_vals\n",
    "        \n",
    "    # Update policy network weights\n",
    "    policy_loss = torch.stack([-log_prob * advantage for log_prob, advantage in zip(log_probs, advantages)]).sum() / T\n",
    "    policy_optimizer.zero_grad()\n",
    "    policy_loss.backward()\n",
    "    policy_optimizer.step() \n",
    "    \n",
    "    # Update value network weights\n",
    "    loss_fn = nn.MSELoss()\n",
    "    value_loss = loss_fn(state_vals, Gs)\n",
    "    value_optimizer.zero_grad()\n",
    "    value_loss.backward()\n",
    "    value_optimizer.step() \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "e98de711",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2023-12-13T17:02:08.465356Z",
     "iopub.status.busy": "2023-12-13T17:02:08.464984Z",
     "iopub.status.idle": "2023-12-13T18:09:10.531975Z",
     "shell.execute_reply": "2023-12-13T18:09:10.530811Z"
    },
    "papermill": {
     "duration": 4022.126983,
     "end_time": "2023-12-13T18:09:10.534507",
     "exception": false,
     "start_time": "2023-12-13T17:02:08.407524",
     "status": "completed"
    },
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/5 [00:00<?, ?it/s]/tmp/ipykernel_19/332058975.py:27: UserWarning: Implicit dimension choice for softmax has been deprecated. Change the call to include dim=X as an argument.\n",
      "  x = self.output_activation(self.output_layer(x))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode: 0\n",
      "The avg. test reward for episode 0 is 18.0 with std. of 9.23038460737146.\n",
      "Episode: 100\n",
      "The avg. test reward for episode 100 is 29.7 with std. of 19.91255885113714.\n",
      "Episode: 200\n",
      "The avg. test reward for episode 200 is 41.2 with std. of 18.3046442194324.\n",
      "Episode: 300\n",
      "The avg. test reward for episode 300 is 39.2 with std. of 25.055139193387053.\n",
      "Episode: 400\n",
      "The avg. test reward for episode 400 is 68.65 with std. of 36.15421828777384.\n",
      "Episode: 500\n",
      "The avg. test reward for episode 500 is 89.2 with std. of 46.56243120800288.\n",
      "Episode: 600\n",
      "The avg. test reward for episode 600 is 96.9 with std. of 48.12161676419444.\n",
      "Episode: 700\n",
      "The avg. test reward for episode 700 is 102.7 with std. of 64.1639306776011.\n",
      "Episode: 800\n",
      "The avg. test reward for episode 800 is 117.05 with std. of 33.72606558731688.\n",
      "Episode: 900\n",
      "The avg. test reward for episode 900 is 88.4 with std. of 43.749742856387165.\n",
      "Episode: 1000\n",
      "The avg. test reward for episode 1000 is 92.75 with std. of 41.16172372483932.\n",
      "Episode: 1100\n",
      "The avg. test reward for episode 1100 is 150.25 with std. of 49.627487343205274.\n",
      "Episode: 1200\n",
      "The avg. test reward for episode 1200 is 170.75 with std. of 46.196184907414164.\n",
      "Episode: 1300\n",
      "The avg. test reward for episode 1300 is 184.8 with std. of 19.9939990997299.\n",
      "Episode: 1400\n",
      "The avg. test reward for episode 1400 is 191.5 with std. of 12.134661099511597.\n",
      "Episode: 1500\n",
      "The avg. test reward for episode 1500 is 161.95 with std. of 28.82442540624184.\n",
      "Episode: 1600\n",
      "The avg. test reward for episode 1600 is 98.5 with std. of 40.0930168483241.\n",
      "Episode: 1700\n",
      "The avg. test reward for episode 1700 is 182.95 with std. of 27.701037886692983.\n",
      "Episode: 1800\n",
      "The avg. test reward for episode 1800 is 171.85 with std. of 29.903636902557515.\n",
      "Episode: 1900\n",
      "The avg. test reward for episode 1900 is 151.75 with std. of 36.661798919311096.\n",
      "Episode: 2000\n",
      "The avg. test reward for episode 2000 is 128.8 with std. of 27.857853470789884.\n",
      "Episode: 2100\n",
      "The avg. test reward for episode 2100 is 196.6 with std. of 14.820256408038292.\n",
      "Episode: 2200\n",
      "The avg. test reward for episode 2200 is 136.55 with std. of 18.969646807465868.\n",
      "Episode: 2300\n",
      "The avg. test reward for episode 2300 is 131.7 with std. of 11.077454581265497.\n",
      "Episode: 2400\n",
      "The avg. test reward for episode 2400 is 150.1 with std. of 23.82834446620243.\n",
      "Episode: 2500\n",
      "The avg. test reward for episode 2500 is 124.0 with std. of 25.39685019840059.\n",
      "Episode: 2600\n",
      "The avg. test reward for episode 2600 is 115.0 with std. of 11.229425630903835.\n",
      "Episode: 2700\n",
      "The avg. test reward for episode 2700 is 158.15 with std. of 17.006689860169732.\n",
      "Episode: 2800\n",
      "The avg. test reward for episode 2800 is 146.85 with std. of 49.442163180831805.\n",
      "Episode: 2900\n",
      "The avg. test reward for episode 2900 is 94.75 with std. of 64.21049369067333.\n",
      "Episode: 3000\n",
      "The avg. test reward for episode 3000 is 174.25 with std. of 41.62916645814566.\n",
      "Episode: 3100\n",
      "The avg. test reward for episode 3100 is 164.1 with std. of 55.43455600976705.\n",
      "Episode: 3200\n",
      "The avg. test reward for episode 3200 is 189.6 with std. of 22.109726366465956.\n",
      "Episode: 3300\n",
      "The avg. test reward for episode 3300 is 177.1 with std. of 29.288052171491366.\n",
      "Episode: 3400\n",
      "The avg. test reward for episode 3400 is 153.95 with std. of 66.60365980935282.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 20%|██        | 1/5 [10:59<43:59, 659.79s/it]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode: 0\n",
      "The avg. test reward for episode 0 is 19.55 with std. of 7.22132259354199.\n",
      "Episode: 100\n",
      "The avg. test reward for episode 100 is 20.55 with std. of 9.851268953794733.\n",
      "Episode: 200\n",
      "The avg. test reward for episode 200 is 24.45 with std. of 11.681074436882934.\n",
      "Episode: 300\n",
      "The avg. test reward for episode 300 is 29.95 with std. of 13.829226297953184.\n",
      "Episode: 400\n",
      "The avg. test reward for episode 400 is 34.75 with std. of 14.777939639882144.\n",
      "Episode: 500\n",
      "The avg. test reward for episode 500 is 40.45 with std. of 24.011403540817852.\n",
      "Episode: 600\n",
      "The avg. test reward for episode 600 is 36.9 with std. of 13.790939054321136.\n",
      "Episode: 700\n",
      "The avg. test reward for episode 700 is 48.35 with std. of 29.97378020870908.\n",
      "Episode: 800\n",
      "The avg. test reward for episode 800 is 108.95 with std. of 43.76582570910778.\n",
      "Episode: 900\n",
      "The avg. test reward for episode 900 is 138.8 with std. of 50.773615195296074.\n",
      "Episode: 1000\n",
      "The avg. test reward for episode 1000 is 127.2 with std. of 47.47904801067519.\n",
      "Episode: 1100\n",
      "The avg. test reward for episode 1100 is 145.3 with std. of 47.47746834025589.\n",
      "Episode: 1200\n",
      "The avg. test reward for episode 1200 is 156.4 with std. of 52.233514145613455.\n",
      "Episode: 1300\n",
      "The avg. test reward for episode 1300 is 137.35 with std. of 36.30877992992879.\n",
      "Episode: 1400\n",
      "The avg. test reward for episode 1400 is 183.25 with std. of 18.228754757250975.\n",
      "Episode: 1500\n",
      "The avg. test reward for episode 1500 is 197.8 with std. of 5.287721626560914.\n",
      "Episode: 1600\n",
      "The avg. test reward for episode 1600 is 200.0 with std. of 0.0.\n",
      "Episode: 1700\n",
      "The avg. test reward for episode 1700 is 200.0 with std. of 0.0.\n",
      "Episode: 1800\n",
      "The avg. test reward for episode 1800 is 197.55 with std. of 5.722543140947038.\n",
      "Episode: 1900\n",
      "The avg. test reward for episode 1900 is 200.0 with std. of 0.0.\n",
      "Episode: 2000\n",
      "The avg. test reward for episode 2000 is 200.0 with std. of 0.0.\n",
      "Episode: 2100\n",
      "The avg. test reward for episode 2100 is 200.0 with std. of 0.0.\n",
      "Episode: 2200\n",
      "The avg. test reward for episode 2200 is 200.0 with std. of 0.0.\n",
      "Episode: 2300\n",
      "The avg. test reward for episode 2300 is 200.0 with std. of 0.0.\n",
      "Episode: 2400\n",
      "The avg. test reward for episode 2400 is 200.0 with std. of 0.0.\n",
      "Episode: 2500\n",
      "The avg. test reward for episode 2500 is 200.0 with std. of 0.0.\n",
      "Episode: 2600\n",
      "The avg. test reward for episode 2600 is 200.0 with std. of 0.0.\n",
      "Episode: 2700\n",
      "The avg. test reward for episode 2700 is 192.75 with std. of 22.984505650546414.\n",
      "Episode: 2800\n",
      "The avg. test reward for episode 2800 is 200.0 with std. of 0.0.\n",
      "Episode: 2900\n",
      "The avg. test reward for episode 2900 is 200.0 with std. of 0.0.\n",
      "Episode: 3000\n",
      "The avg. test reward for episode 3000 is 196.95 with std. of 13.294641777799056.\n",
      "Episode: 3100\n",
      "The avg. test reward for episode 3100 is 200.0 with std. of 0.0.\n",
      "Episode: 3200\n",
      "The avg. test reward for episode 3200 is 200.0 with std. of 0.0.\n",
      "Episode: 3300\n",
      "The avg. test reward for episode 3300 is 200.0 with std. of 0.0.\n",
      "Episode: 3400\n",
      "The avg. test reward for episode 3400 is 200.0 with std. of 0.0.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 40%|████      | 2/5 [24:55<38:10, 763.49s/it]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode: 0\n",
      "The avg. test reward for episode 0 is 22.2 with std. of 13.22724461102916.\n",
      "Episode: 100\n",
      "The avg. test reward for episode 100 is 17.9 with std. of 5.7436921923097515.\n",
      "Episode: 200\n",
      "The avg. test reward for episode 200 is 20.25 with std. of 10.976679825885421.\n",
      "Episode: 300\n",
      "The avg. test reward for episode 300 is 21.8 with std. of 12.085528536228773.\n",
      "Episode: 400\n",
      "The avg. test reward for episode 400 is 24.7 with std. of 17.782294565100422.\n",
      "Episode: 500\n",
      "The avg. test reward for episode 500 is 24.8 with std. of 9.91766101457395.\n",
      "Episode: 600\n",
      "The avg. test reward for episode 600 is 33.15 with std. of 27.4904983585238.\n",
      "Episode: 700\n",
      "The avg. test reward for episode 700 is 52.1 with std. of 38.204580877167075.\n",
      "Episode: 800\n",
      "The avg. test reward for episode 800 is 112.35 with std. of 53.414674949867475.\n",
      "Episode: 900\n",
      "The avg. test reward for episode 900 is 142.85 with std. of 57.95280407365979.\n",
      "Episode: 1000\n",
      "The avg. test reward for episode 1000 is 183.7 with std. of 26.77704240576244.\n",
      "Episode: 1100\n",
      "The avg. test reward for episode 1100 is 147.1 with std. of 37.357596282416246.\n",
      "Episode: 1200\n",
      "The avg. test reward for episode 1200 is 195.25 with std. of 17.386417112217227.\n",
      "Episode: 1300\n",
      "The avg. test reward for episode 1300 is 197.2 with std. of 9.21737489744233.\n",
      "Episode: 1400\n",
      "The avg. test reward for episode 1400 is 199.95 with std. of 0.21794494717703367.\n",
      "Episode: 1500\n",
      "The avg. test reward for episode 1500 is 189.9 with std. of 20.67583130130443.\n",
      "Episode: 1600\n",
      "The avg. test reward for episode 1600 is 196.25 with std. of 16.345871038277526.\n",
      "Episode: 1700\n",
      "The avg. test reward for episode 1700 is 189.75 with std. of 22.22357981964202.\n",
      "Episode: 1800\n",
      "The avg. test reward for episode 1800 is 198.5 with std. of 6.5383484153110105.\n",
      "Episode: 1900\n",
      "The avg. test reward for episode 1900 is 200.0 with std. of 0.0.\n",
      "Episode: 2000\n",
      "The avg. test reward for episode 2000 is 199.8 with std. of 0.8717797887081347.\n",
      "Episode: 2100\n",
      "The avg. test reward for episode 2100 is 196.35 with std. of 8.793605631366464.\n",
      "Episode: 2200\n",
      "The avg. test reward for episode 2200 is 200.0 with std. of 0.0.\n",
      "Episode: 2300\n",
      "The avg. test reward for episode 2300 is 200.0 with std. of 0.0.\n",
      "Episode: 2400\n",
      "The avg. test reward for episode 2400 is 199.7 with std. of 1.3076696830622017.\n",
      "Episode: 2500\n",
      "The avg. test reward for episode 2500 is 197.5 with std. of 10.897247358851684.\n",
      "Episode: 2600\n",
      "The avg. test reward for episode 2600 is 197.35 with std. of 8.076354375583083.\n",
      "Episode: 2700\n",
      "The avg. test reward for episode 2700 is 200.0 with std. of 0.0.\n",
      "Episode: 2800\n",
      "The avg. test reward for episode 2800 is 197.0 with std. of 13.076696830622021.\n",
      "Episode: 2900\n",
      "The avg. test reward for episode 2900 is 197.6 with std. of 10.461357464497617.\n",
      "Episode: 3000\n",
      "The avg. test reward for episode 3000 is 195.1 with std. of 12.185647295076285.\n",
      "Episode: 3100\n",
      "The avg. test reward for episode 3100 is 199.55 with std. of 1.9615045245933027.\n",
      "Episode: 3200\n",
      "The avg. test reward for episode 3200 is 200.0 with std. of 0.0.\n",
      "Episode: 3300\n",
      "The avg. test reward for episode 3300 is 200.0 with std. of 0.0.\n",
      "Episode: 3400\n",
      "The avg. test reward for episode 3400 is 191.65 with std. of 17.49935713104913.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 60%|██████    | 3/5 [39:01<26:41, 800.97s/it]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode: 0\n",
      "The avg. test reward for episode 0 is 20.7 with std. of 8.087644898238299.\n",
      "Episode: 100\n",
      "The avg. test reward for episode 100 is 22.35 with std. of 7.35713938973566.\n",
      "Episode: 200\n",
      "The avg. test reward for episode 200 is 21.25 with std. of 8.797016539713905.\n",
      "Episode: 300\n",
      "The avg. test reward for episode 300 is 28.6 with std. of 13.009227494359532.\n",
      "Episode: 400\n",
      "The avg. test reward for episode 400 is 32.15 with std. of 16.2827362565387.\n",
      "Episode: 500\n",
      "The avg. test reward for episode 500 is 33.55 with std. of 22.992335679525908.\n",
      "Episode: 600\n",
      "The avg. test reward for episode 600 is 55.9 with std. of 31.059459106687612.\n",
      "Episode: 700\n",
      "The avg. test reward for episode 700 is 42.4 with std. of 23.467850348934817.\n",
      "Episode: 800\n",
      "The avg. test reward for episode 800 is 67.15 with std. of 23.343682228817286.\n",
      "Episode: 900\n",
      "The avg. test reward for episode 900 is 120.35 with std. of 63.66888957724957.\n",
      "Episode: 1000\n",
      "The avg. test reward for episode 1000 is 133.1 with std. of 56.307992327910256.\n",
      "Episode: 1100\n",
      "The avg. test reward for episode 1100 is 153.6 with std. of 46.157772909879434.\n",
      "Episode: 1200\n",
      "The avg. test reward for episode 1200 is 163.75 with std. of 54.72556532371319.\n",
      "Episode: 1300\n",
      "The avg. test reward for episode 1300 is 173.7 with std. of 44.6274579155031.\n",
      "Episode: 1400\n",
      "The avg. test reward for episode 1400 is 151.35 with std. of 43.63630942231481.\n",
      "Episode: 1500\n",
      "The avg. test reward for episode 1500 is 194.2 with std. of 22.27913822390803.\n",
      "Episode: 1600\n",
      "The avg. test reward for episode 1600 is 196.85 with std. of 13.730531672153122.\n",
      "Episode: 1700\n",
      "The avg. test reward for episode 1700 is 199.85 with std. of 0.6538348415311008.\n",
      "Episode: 1800\n",
      "The avg. test reward for episode 1800 is 197.8 with std. of 5.045790324617146.\n",
      "Episode: 1900\n",
      "The avg. test reward for episode 1900 is 192.45 with std. of 20.648183939513906.\n",
      "Episode: 2000\n",
      "The avg. test reward for episode 2000 is 200.0 with std. of 0.0.\n",
      "Episode: 2100\n",
      "The avg. test reward for episode 2100 is 200.0 with std. of 0.0.\n",
      "Episode: 2200\n",
      "The avg. test reward for episode 2200 is 200.0 with std. of 0.0.\n",
      "Episode: 2300\n",
      "The avg. test reward for episode 2300 is 200.0 with std. of 0.0.\n",
      "Episode: 2400\n",
      "The avg. test reward for episode 2400 is 200.0 with std. of 0.0.\n",
      "Episode: 2500\n",
      "The avg. test reward for episode 2500 is 200.0 with std. of 0.0.\n",
      "Episode: 2600\n",
      "The avg. test reward for episode 2600 is 200.0 with std. of 0.0.\n",
      "Episode: 2700\n",
      "The avg. test reward for episode 2700 is 200.0 with std. of 0.0.\n",
      "Episode: 2800\n",
      "The avg. test reward for episode 2800 is 200.0 with std. of 0.0.\n",
      "Episode: 2900\n",
      "The avg. test reward for episode 2900 is 199.5 with std. of 2.179449471770337.\n",
      "Episode: 3000\n",
      "The avg. test reward for episode 3000 is 198.4 with std. of 6.974238309665077.\n",
      "Episode: 3100\n",
      "The avg. test reward for episode 3100 is 200.0 with std. of 0.0.\n",
      "Episode: 3200\n",
      "The avg. test reward for episode 3200 is 197.95 with std. of 8.935742834258381.\n",
      "Episode: 3300\n",
      "The avg. test reward for episode 3300 is 200.0 with std. of 0.0.\n",
      "Episode: 3400\n",
      "The avg. test reward for episode 3400 is 200.0 with std. of 0.0.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      " 80%|████████  | 4/5 [52:44<13:29, 809.66s/it]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode: 0\n",
      "The avg. test reward for episode 0 is 18.65 with std. of 7.8439467106807905.\n",
      "Episode: 100\n",
      "The avg. test reward for episode 100 is 18.85 with std. of 9.613922196481518.\n",
      "Episode: 200\n",
      "The avg. test reward for episode 200 is 21.0 with std. of 9.15969431804359.\n",
      "Episode: 300\n",
      "The avg. test reward for episode 300 is 20.05 with std. of 9.588925904396175.\n",
      "Episode: 400\n",
      "The avg. test reward for episode 400 is 20.15 with std. of 8.404016896698863.\n",
      "Episode: 500\n",
      "The avg. test reward for episode 500 is 18.45 with std. of 6.938839960685071.\n",
      "Episode: 600\n",
      "The avg. test reward for episode 600 is 29.75 with std. of 11.16187708228325.\n",
      "Episode: 700\n",
      "The avg. test reward for episode 700 is 66.9 with std. of 42.462807255291075.\n",
      "Episode: 800\n",
      "The avg. test reward for episode 800 is 139.4 with std. of 50.64523669606057.\n",
      "Episode: 900\n",
      "The avg. test reward for episode 900 is 187.3 with std. of 25.241038013520757.\n",
      "Episode: 1000\n",
      "The avg. test reward for episode 1000 is 188.45 with std. of 30.332284780411776.\n",
      "Episode: 1100\n",
      "The avg. test reward for episode 1100 is 185.55 with std. of 30.554009556848666.\n",
      "Episode: 1200\n",
      "The avg. test reward for episode 1200 is 173.2 with std. of 27.023323259732507.\n",
      "Episode: 1300\n",
      "The avg. test reward for episode 1300 is 197.2 with std. of 12.204917041913887.\n",
      "Episode: 1400\n",
      "The avg. test reward for episode 1400 is 197.05 with std. of 8.963676700997198.\n",
      "Episode: 1500\n",
      "The avg. test reward for episode 1500 is 199.55 with std. of 1.961504524593303.\n",
      "Episode: 1600\n",
      "The avg. test reward for episode 1600 is 200.0 with std. of 0.0.\n",
      "Episode: 1700\n",
      "The avg. test reward for episode 1700 is 199.5 with std. of 1.5329709716755893.\n",
      "Episode: 1800\n",
      "The avg. test reward for episode 1800 is 91.5 with std. of 38.13462993133669.\n",
      "Episode: 1900\n",
      "The avg. test reward for episode 1900 is 196.9 with std. of 7.680494775728969.\n",
      "Episode: 2000\n",
      "The avg. test reward for episode 2000 is 200.0 with std. of 0.0.\n",
      "Episode: 2100\n",
      "The avg. test reward for episode 2100 is 200.0 with std. of 0.0.\n",
      "Episode: 2200\n",
      "The avg. test reward for episode 2200 is 200.0 with std. of 0.0.\n",
      "Episode: 2300\n",
      "The avg. test reward for episode 2300 is 200.0 with std. of 0.0.\n",
      "Episode: 2400\n",
      "The avg. test reward for episode 2400 is 200.0 with std. of 0.0.\n",
      "Episode: 2500\n",
      "The avg. test reward for episode 2500 is 200.0 with std. of 0.0.\n",
      "Episode: 2600\n",
      "The avg. test reward for episode 2600 is 200.0 with std. of 0.0.\n",
      "Episode: 2700\n",
      "The avg. test reward for episode 2700 is 200.0 with std. of 0.0.\n",
      "Episode: 2800\n",
      "The avg. test reward for episode 2800 is 200.0 with std. of 0.0.\n",
      "Episode: 2900\n",
      "The avg. test reward for episode 2900 is 199.95 with std. of 0.2179449471770337.\n",
      "Episode: 3000\n",
      "The avg. test reward for episode 3000 is 193.25 with std. of 11.827404618089295.\n",
      "Episode: 3100\n",
      "The avg. test reward for episode 3100 is 199.8 with std. of 0.8717797887081347.\n",
      "Episode: 3200\n",
      "The avg. test reward for episode 3200 is 199.3 with std. of 3.0512292604784714.\n",
      "Episode: 3300\n",
      "The avg. test reward for episode 3300 is 200.0 with std. of 0.0.\n",
      "Episode: 3400\n",
      "The avg. test reward for episode 3400 is 200.0 with std. of 0.0.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 5/5 [1:07:01<00:00, 804.35s/it]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Actor Critic Learning Curve')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "policy_lr = 5e-4\n",
    "critic_lr = 1e-4\n",
    "n = 100 # number of time step to use immediate reward\n",
    "returns = np.zeros((num_seeds, l)) # dim: (5 ,35)\n",
    "\n",
    "for i in tqdm.tqdm(range(num_seeds)):\n",
    "    reward_means = []\n",
    "\n",
    "    # Define policy and value networks\n",
    "    policy_net = NeuralNet(nS, nA, torch.nn.Softmax())\n",
    "    policy_net_optimizer = optim.Adam(policy_net.parameters(), lr=policy_lr)\n",
    "    value_net = NeuralNet(nS, 1, torch.nn.ReLU())\n",
    "    value_net_optimizer = optim.Adam(value_net.parameters(), lr=critic_lr)\n",
    "    \n",
    "    for m in range(num_episodes):\n",
    "        train_actor_critic(env, policy_net, policy_net_optimizer, value_net, value_net_optimizer, gamma=gamma)\n",
    "        if m % 100 == 0:\n",
    "            print(\"Episode: {}\".format(m))\n",
    "            G = np.zeros(20)\n",
    "            for k in range(20):\n",
    "                g = evaluate_policy(env, policy_net)\n",
    "                G[k] = g\n",
    "\n",
    "            reward_mean = G.mean()\n",
    "            reward_sd = G.std()\n",
    "            print(\"The avg. test reward for episode {0} is {1} with std. of {2}.\".format(m, reward_mean, reward_sd))\n",
    "            reward_means.append(reward_mean)\n",
    "    returns[i] = np.array(reward_means)\n",
    "\n",
    "\n",
    "# Plot the performance over iterations\n",
    "ks = np.arange(l)*100\n",
    "avs = np.mean(returns, axis=0)\n",
    "maxs = np.max(returns, axis=0)\n",
    "mins = np.min(returns, axis=0)\n",
    "\n",
    "plt.fill_between(ks, mins, maxs, alpha=0.1)\n",
    "plt.plot(ks, avs, '-o', markersize=1)\n",
    "\n",
    "plt.xlabel('Episode', fontsize = 15)\n",
    "plt.ylabel('Return', fontsize = 15)\n",
    "\n",
    "plt.title(\"Actor Critic Learning Curve\", fontsize = 24)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "120f26e3",
   "metadata": {
    "papermill": {
     "duration": 0.079333,
     "end_time": "2023-12-13T18:09:10.694953",
     "exception": false,
     "start_time": "2023-12-13T18:09:10.615620",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "In the CartPole-v0 environment with the specified hyperparameters, the actor-critic method does not outperform REINFORCE with a baseline. It takes a longer time to converge to the best score, and the variance around the performance is greater compared to REINFORCE with a baseline. This could be attributed to suboptimal hyperparameters (such as learning rate, the number of immediate reward steps, and discount rate) used in this code. However, this outcome also highlights the inherent challenges of actor-critic methods, which involve training two networks, as opposed to the simplicity of tuning a single value network in REINFORCE with a baseline.\n",
    "\n",
    "Another possible explanation is that the value function in this environment is relatively straightforward, and the use of bootstrapping in actor-critic does not have a significant advantage over REINFORCE with a baseline. In environments with relatively simple state and action spaces, where complexity is not a significant factor, REINFORCE with a baseline might be more effective. Actor-critic methods, with their additional complexity of maintaining a value function, might introduce unnecessary complications in such scenarios."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1ee238f",
   "metadata": {
    "papermill": {
     "duration": 0.079365,
     "end_time": "2023-12-13T18:09:10.852619",
     "exception": false,
     "start_time": "2023-12-13T18:09:10.773254",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Summary"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2133e9a",
   "metadata": {
    "papermill": {
     "duration": 0.083447,
     "end_time": "2023-12-13T18:09:11.015066",
     "exception": false,
     "start_time": "2023-12-13T18:09:10.931619",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "In this notebook, we learned three fundamental policy gradient methods: REINFORCE, REINFORCE with baseline, and Actor Critic. The Policy Gradient Theorem provides the foundation of the policy gradient methods by offering a way to estimate the gradient of the objective function. REINFORCE uses the sampled return to learn the optimal policy. REINFORCE with baseline introduces a baseline estimate of the value at each state to stabilize and accelerate the learning. Actor Critic uses bootstrapping to further improve the learning performance (although this was not very effective for this notebook case).\n",
    "Depending on the problem setting, it would be important to carefully consider which approach would be more effective, whether using methods based on value function estimates or using policy gradient methods."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2efe5091",
   "metadata": {
    "papermill": {
     "duration": 0.078843,
     "end_time": "2023-12-13T18:09:11.189130",
     "exception": false,
     "start_time": "2023-12-13T18:09:11.110287",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Ref"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa4bf5a4",
   "metadata": {
    "papermill": {
     "duration": 0.080268,
     "end_time": "2023-12-13T18:09:11.348559",
     "exception": false,
     "start_time": "2023-12-13T18:09:11.268291",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "- Sutton, R. S., & Barto, A. G. (2018). Reinforcement learning: An introduction. MIT press.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ee4b7400",
   "metadata": {
    "papermill": {
     "duration": 0.081444,
     "end_time": "2023-12-13T18:09:11.510158",
     "exception": false,
     "start_time": "2023-12-13T18:09:11.428714",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kaggle": {
   "accelerator": "none",
   "dataSources": [],
   "dockerImageVersionId": 30626,
   "isGpuEnabled": false,
   "isInternetEnabled": true,
   "language": "python",
   "sourceType": "notebook"
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.12"
  },
  "papermill": {
   "default_parameters": {},
   "duration": 7521.42744,
   "end_time": "2023-12-13T18:09:12.524464",
   "environment_variables": {},
   "exception": null,
   "input_path": "__notebook__.ipynb",
   "output_path": "__notebook__.ipynb",
   "parameters": {},
   "start_time": "2023-12-13T16:03:51.097024",
   "version": "2.4.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}