TD/Q-Learning.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import gym\n",
    "import itertools\n",
    "import matplotlib\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import sys\n",
    "\n",
    "if \"../\" not in sys.path:\n",
    "  sys.path.append(\"../\") \n",
    "\n",
    "from collections import defaultdict\n",
    "from lib.envs.cliff_walking import CliffWalkingEnv\n",
    "from lib import plotting\n",
    "\n",
    "matplotlib.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "env = CliffWalkingEnv()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def make_epsilon_greedy_policy(Q, epsilon, nA):\n",
    "    \"\"\"\n",
    "    Creates an epsilon-greedy policy based on a given Q-function and epsilon.\n",
    "    \n",
    "    Args:\n",
    "        Q: A dictionary that maps from state -> action-values.\n",
    "            Each value is a numpy array of length nA (see below)\n",
    "        epsilon: The probability to select a random action. Float between 0 and 1.\n",
    "        nA: Number of actions in the environment.\n",
    "    \n",
    "    Returns:\n",
    "        A function that takes the observation as an argument and returns\n",
    "        the probabilities for each action in the form of a numpy array of length nA.\n",
    "    \n",
    "    \"\"\"\n",
    "    def policy_fn(observation):\n",
    "        A = np.ones(nA, dtype=float) * epsilon / nA\n",
    "        best_action = np.argmax(Q[observation])\n",
    "        A[best_action] += (1.0 - epsilon)\n",
    "        return A\n",
    "    return policy_fn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def q_learning(env, num_episodes, discount_factor=1.0, alpha=0.5, epsilon=0.1):\n",
    "    \"\"\"\n",
    "    Q-Learning algorithm: Off-policy TD control. Finds the optimal greedy policy\n",
    "    while following an epsilon-greedy policy\n",
    "    \n",
    "    Args:\n",
    "        env: OpenAI environment.\n",
    "        num_episodes: Number of episodes to run for.\n",
    "        discount_factor: Gamma discount factor.\n",
    "        alpha: TD learning rate.\n",
    "        epsilon: Chance to sample a random action. Float between 0 and 1.\n",
    "    \n",
    "    Returns:\n",
    "        A tuple (Q, episode_lengths).\n",
    "        Q is the optimal action-value function, a dictionary mapping state -> action values.\n",
    "        stats is an EpisodeStats object with two numpy arrays for episode_lengths and episode_rewards.\n",
    "    \"\"\"\n",
    "    \n",
    "    # The final action-value function.\n",
    "    # A nested dictionary that maps state -> (action -> action-value).\n",
    "    Q = defaultdict(lambda: np.zeros(env.action_space.n))\n",
    "\n",
    "    # Keeps track of useful statistics\n",
    "    stats = plotting.EpisodeStats(\n",
    "        episode_lengths=np.zeros(num_episodes),\n",
    "        episode_rewards=np.zeros(num_episodes))    \n",
    "    \n",
    "    # The policy we're following\n",
    "    policy = make_epsilon_greedy_policy(Q, epsilon, env.action_space.n)\n",
    "    \n",
    "    for i_episode in range(num_episodes):\n",
    "        # Print out which episode we're on, useful for debugging.\n",
    "        if (i_episode + 1) % 100 == 0:\n",
    "            print(\"\\rEpisode {}/{}.\".format(i_episode + 1, num_episodes), end=\"\")\n",
    "            sys.stdout.flush()\n",
    "        \n",
    "        # Implement this!\n",
    "    \n",
    "    return Q, stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode 500/500."
     ]
    }
   ],
   "source": [
    "Q, stats = q_learning(env, 500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAn4AAAFZCAYAAAAGkSJzAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAsguAHAABgEQQ/AAAAi/h/v40/Klo6ZhYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a3839b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAn4AAAFZCAYAAAAGkSJzAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niNjEvwCXctN9U+ogMQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a3bb908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAnQAAAFZCAYAAAARs7K6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nsDkCHQAAgM39P+XhbrHG6s8eAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a53d0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotting.plot_episode_stats(stats)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}