experiments.ipynb

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  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "M8tf7QvNbIOC"
      },
      "source": [
        "import tensorflow as tf\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import scipy.stats\n",
        "import tqdm\n",
        "from scipy.ndimage import gaussian_filter1d\n",
        "import colorsys\n",
        "import matplotlib.colors\n",
        "from matplotlib.ticker import (MultipleLocator, FormatStrFormatter, AutoMinorLocator)\n",
        "from matplotlib import gridspec\n",
        "import matplotlib.patches"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Relabeling with Failures [Fig. 6]"
      ],
      "metadata": {
        "id": "HFClseMuwFDc"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "height = 1\n",
        "width = 11  # should be an odd number\n",
        "num_s = height * width\n",
        "start_i, start_j = (0, width // 2)\n",
        "goals = [(0, 0),\n",
        "         (0, width - 1)]\n",
        "num_a = 3\n",
        "gamma = 0.9\n",
        "\n",
        "rc_params = {\n",
        "             'xtick.direction': 'inout',\n",
        "             'ytick.direction': 'inout',\n",
        "             'font.family': 'sans-serif',\n",
        "             'font.sans-serif': 'Roboto',\n",
        "             'legend.frameon': False,\n",
        "}\n",
        "matplotlib.rcParams.update(rc_params)\n",
        "c_vec = plt.rcParams['axes.prop_cycle'].by_key()['color']\n",
        "\n",
        "\n",
        "def step(s, a):\n",
        "  j = s\n",
        "  if a == 0:\n",
        "    j = max(0, j - 1)\n",
        "  elif a == 1:\n",
        "    j = j\n",
        "  else:\n",
        "    assert a == 2\n",
        "    j = min(width - 1, j + 1)\n",
        "  s = j\n",
        "  return s\n",
        "\n",
        "max_episode_steps = 7\n",
        "def evaluate(pi):\n",
        "  num_episodes = 100\n",
        "  avg_time = []\n",
        "  for goal_i, goal_j in goals:\n",
        "    vec = []\n",
        "    for _ in range(num_episodes):\n",
        "      s = np.ravel_multi_index((start_i, start_j), (height, width))\n",
        "      g = np.ravel_multi_index((goal_i, goal_j), (height, width))\n",
        "      s_vec = []\n",
        "      for t in range(max_episode_steps):\n",
        "        s_vec.append(s)\n",
        "        a = np.random.choice(num_a, p=pi[s, :, g])\n",
        "        s = step(s, a)\n",
        "      if goal_j == 0:\n",
        "        vec.append(width // 2 - np.mean(s_vec))\n",
        "      else:\n",
        "        vec.append(np.mean(s_vec) - width // 2)\n",
        "    avg_time.append(np.mean(vec))\n",
        "  return avg_time\n",
        "\n",
        "\n",
        "num_episodes_vec = [1, 3, 10, 30, 100]\n",
        "results = {}\n",
        "for num_episodes in tqdm.tqdm(num_episodes_vec):\n",
        "  for use_fail in [True, False]:\n",
        "    print(num_episodes, use_fail)\n",
        "    result_vec = []\n",
        "    for _ in range(100):\n",
        "      pi_ocbc = np.ones((num_s, num_a, num_s)) / num_a\n",
        "      counts = np.zeros((num_s, num_a, num_s)) + 0.01  # [s, a, ns]\n",
        "      for _ in range(num_episodes):\n",
        "        vec = []\n",
        "        s = start_j\n",
        "        i = np.random.choice(2)\n",
        "        g = np.ravel_multi_index(goals[i], (height, width))\n",
        "        for _ in range(max_episode_steps):\n",
        "          a = np.random.choice(num_a, p=pi_ocbc[s, :, g])\n",
        "          vec.append((s, a))\n",
        "          s = step(s, a)\n",
        "        vec = np.array(vec)\n",
        "        for i in range(len(vec)):\n",
        "          for j in range(i, min(i + 20, len(vec))):\n",
        "            s1, a1 = vec[i]\n",
        "            s2, a2 = vec[j]\n",
        "            weight = gamma**(j - i)\n",
        "            counts[s1, a1, s2] += weight\n",
        "\n",
        "        if not use_fail:\n",
        "          counts[:, :, :width // 2] = counts[:, :, :width//2].sum(-1)[:, :, None]\n",
        "          counts[:, :, width // 2+1:] = counts[:, :, width//2+1:].sum(-1)[:, :, None]\n",
        "        p_sag = counts / counts.sum()\n",
        "        p_a_given_sg = p_sag / np.sum(p_sag, axis=1)[:, None, :]\n",
        "        pi_ocbc = p_a_given_sg\n",
        "      result_vec.append(np.mean(evaluate(pi_ocbc)))\n",
        "    results[(num_episodes, use_fail)] = result_vec\n",
        "\n",
        "\n",
        "custom_c_vec = [c_vec[2], c_vec[4]]\n",
        "plt.figure(figsize=(4, 2))\n",
        "for use_fail in [True, False]:\n",
        "  y = [results[(num_episodes, use_fail)] for num_episodes in num_episodes_vec]\n",
        "  y = np.array(y).reshape((len(num_episodes_vec), 10, 10)).mean(-1)\n",
        "  mu = np.mean(y, axis=-1)\n",
        "  std = np.std(y, axis=-1)\n",
        "  a, b, c = plt.errorbar(num_episodes_vec, mu, yerr=std,\n",
        "               marker='o' if use_fail else 's',\n",
        "               elinewidth=0.5, c=custom_c_vec[int(use_fail)],\n",
        "               linewidth=1, markersize=4)\n",
        "  c[0].set_capstyle('round')\n",
        "  plt.plot([np.nan], [np.nan],\n",
        "            label='tasks = {left, right, fail}' if use_fail else 'tasks = {left, right}',\n",
        "            marker='o' if use_fail else 's',\n",
        "           c=custom_c_vec[int(use_fail)],\n",
        "            linewidth=1, markersize=4)\n",
        "\n",
        "plt.xlabel('number of episodes', fontsize=12)\n",
        "plt.ylabel('rewards', fontsize=12)\n",
        "plt.xscale('log')\n",
        "\n",
        "plt.text(2, 1, 'tasks = {left, right}', c=custom_c_vec[0])\n",
        "plt.text(5.5, 1.6, 'tasks = {left, right, fail}', c=custom_c_vec[1])\n",
        "\n",
        "plt.gca().yaxis.set_major_locator(MultipleLocator(1))\n",
        "plt.gca().yaxis.set_minor_locator(MultipleLocator(0.5))\n",
        "\n",
        "for axis in [plt.gca().xaxis, plt.gca().yaxis]:\n",
        "  for i in axis.get_majorticklines():\n",
        "    i._marker._capstyle = 'round'\n",
        "  for i in axis.get_minorticklines():\n",
        "    i._marker._capstyle = 'round'\n",
        "\n",
        "filename = 'fig_6.pdf'\n",
        "plt.savefig(filename, dpi=200, bbox_inches='tight')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "height": 388
        },
        "id": "iDffWWjdwID1",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1643236985959,
          "user_tz": 420,
          "elapsed": 69479,
          "user": {
          }
        },
        "outputId": "faaf976d-65a4-46fb-d6d9-0960ae60e53f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "\r  0%|          | 0/5 [00:00<?, ?it/s]"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1 True\n",
            "1"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "\r 20%|██        | 1/5 [00:10<00:43, 10.94s/it]"
          ]
        },
        {
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          "name": "stdout",
          "text": [
            " False\n",
            "3 True\n",
            "3"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "\r 40%|████      | 2/5 [00:22<00:33, 11.11s/it]"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            " False\n",
            "10 True\n",
            "10"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "\r 60%|██████    | 3/5 [00:34<00:23, 11.54s/it]"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            " False\n",
            "30 True\n",
            "30"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "\r 80%|████████  | 4/5 [00:47<00:12, 12.39s/it]"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            " False\n",
            "100 True\n",
            "100"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 5/5 [01:07<00:00, 13.59s/it]"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            " False\n"
          ]
        },
        {
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          "text": [
            "\n"
          ]
        },
        {
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              "<a download='fig_6.pdf' id='id_862642745'>Download fig_6.pdf</a>"
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\");\n",
              "      const arr = new Uint8Array(chunk.length);\n",
              "      for(let i=0; i<chunk.length; ++i) {\n",
              "        arr[i] = chunk.charCodeAt(i);\n",
              "      }\n",
              "      window[\"id_862642746\"].push(arr);\n",
              "      return true;\n",
              "    })();\n",
              "    \n",
              "//# sourceURL=js_38a73bd863"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "\n",
              "    (function() {\n",
              "      const blob = new Blob(window[\"id_862642746\"], {type: \"\"});\n",
              "      window[\"id_862642746\"] = URL.createObjectURL(blob);\n",
              "      return true;\n",
              "    })();\n",
              "  \n",
              "//# sourceURL=js_5c2b05e11c"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "window[\"5407a214-7ef9-11ec-a5f4-e78f1c3429d8\"] = document.getElementById(\"id_862642745\");\n",
              "//# sourceURL=js_2d556496a0"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "window[\"5407cbc2-7ef9-11ec-a5f4-e78f1c3429d8\"] = window[\"5407a214-7ef9-11ec-a5f4-e78f1c3429d8\"].setAttribute(\"href\", id_862642746);\n",
              "//# sourceURL=js_0c5ca7c929"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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AEF8aak0wiJbj07RlYEUJ1fQLFrOF08cryNpbTNb+YoJC/Rg9LZqF/zmFiOHB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\nPx4QnY3kWAc3AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 400x200 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Bandit Problem [Fig. 3]"
      ],
      "metadata": {
        "id": "fa7e8a0dypPB"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "### Show the improvement steps\n",
        "\n",
        "rc_params = {\n",
        "             'xtick.direction': 'inout',\n",
        "             'ytick.direction': 'inout',\n",
        "             'font.family': 'sans-serif',\n",
        "             'font.sans-serif': 'Roboto',\n",
        "             'legend.frameon': False,\n",
        "}\n",
        "matplotlib.rcParams.update(rc_params)\n",
        "\n",
        "c_vec = plt.rcParams['axes.prop_cycle'].by_key()['color']\n",
        "def p_to_xy(p):\n",
        "  return xy\n",
        "p_g_given_a = np.array([\n",
        "  [0.33, 0, 0],\n",
        "  [0.33, 1, 0.6],\n",
        "  [0.34, 0, 0.4]])  # [num_goals, num_actions]\n",
        "p_a_given_g = np.array([  # initial policy\n",
        "  [0.8, 0.1, 0.1],\n",
        "  [0.1, 0.8, 0.1],\n",
        "  [0.1, 0.1, 0.8]])  # [num_goals, num_actions]\n",
        "p_a_given_g_orig = p_a_given_g.copy()\n",
        "p_g = np.ones(3) / 3\n",
        "\n",
        "## compute the new policy\n",
        "p_a = np.sum(p_a_given_g * p_g[:, None], axis=0)\n",
        "p_ag = p_g_given_a * p_a[None]\n",
        "p_g_new = p_ag.sum(axis=1)\n",
        "p_a_given_g_old = p_a_given_g\n",
        "p_a_given_g = p_ag / p_g_new[:, None]  # OCBC\n",
        "\n",
        "### plotting\n",
        "plt.figure(figsize=(12.5, 4))\n",
        "outer_gs = gridspec.GridSpec(1, 2, width_ratios=(3, 1), wspace=0.02)\n",
        "gs1 = gridspec.GridSpecFromSubplotSpec(1, 3, subplot_spec = outer_gs[0], hspace=0, wspace=0)\n",
        "gs2 = gridspec.GridSpecFromSubplotSpec(1, 1, subplot_spec = outer_gs[1], hspace=0, wspace=0)\n",
        "\n",
        "\n",
        "plt.subplot(gs1[0])\n",
        "for g in range(3):\n",
        "  p = p_a_given_g_old[g]\n",
        "  plt.plot([p[0]], [p[1]], 'o', ms=10, c=c_vec[g], alpha=0.5)\n",
        "  delta = p_a - p\n",
        "  plt.arrow(p[0], p[1], delta[0], delta[1], length_includes_head=True,\n",
        "            width=0.01, fc='k', linewidth=0)\n",
        "  \n",
        "  z = np.eye(3)[g]\n",
        "  plt.plot([z[0]], [z[1]], marker='*', c=c_vec[g], markersize=20, alpha=0.5)\n",
        "\n",
        "plt.plot([np.nan], [np.nan], 'o', ms=5, c='k', alpha=0.5,\n",
        "          label='current policy \\nfor task $e_i$')\n",
        "plt.plot([np.nan], [np.nan], '*', ms=10, c='k', alpha=0.5,\n",
        "          label='optimal policy \\nfor task $e_i$')\n",
        "plt.legend(loc='upper right', frameon=True, fontsize=8)\n",
        "\n",
        "plt.gca().set_aspect('equal')\n",
        "plt.xlabel('$\\pi(a = a_1)$', fontsize=14)\n",
        "plt.ylabel('$\\pi(a = a_2)$', fontsize=14)\n",
        "plt.title('averaging step')\n",
        "plt.text(0.05, 0.95, 'task $e_2$', fontsize=12, va='center')\n",
        "plt.text(0.65, 0, 'task $e_1$', fontsize=12, va='center')\n",
        "plt.text(0.1, 0, 'task $e_3$', fontsize=12, va='center')\n",
        "plt.gca().yaxis.set_major_locator(MultipleLocator(1))\n",
        "plt.gca().yaxis.set_minor_locator(MultipleLocator(0.2))\n",
        "plt.gca().xaxis.set_major_locator(MultipleLocator(1))\n",
        "plt.gca().xaxis.set_minor_locator(MultipleLocator(0.2))\n",
        "plt.xlim([-0.1, 1.1])\n",
        "plt.ylim([-0.1, 1.1])\n",
        "\n",
        "\n",
        "plt.subplot(gs1[1])\n",
        "plt.gca().set_aspect('equal')\n",
        "plt.xlabel('$\\pi(a = a_1)$', fontsize=14)\n",
        "for g in range(3):\n",
        "  p = p_a_given_g[g]\n",
        "  plt.plot([p[0]], [p[1]], 'o', ms=10, c=c_vec[g], alpha=0.5)  \n",
        "  z = np.eye(3)[g]\n",
        "  plt.plot([z[0]], [z[1]], marker='*', c=c_vec[g], markersize=20, alpha=0.5)\n",
        "  delta = p - p_a\n",
        "  plt.arrow(p_a[0], p_a[1], delta[0], delta[1], length_includes_head=True,\n",
        "            width=0.01, fc='k', linewidth=0)\n",
        "\n",
        "plt.title('improvement step')\n",
        "plt.gca().yaxis.set_major_locator(MultipleLocator(1))\n",
        "plt.gca().yaxis.set_minor_locator(MultipleLocator(0.2))\n",
        "plt.gca().yaxis.set_major_formatter(FormatStrFormatter(''))\n",
        "plt.gca().xaxis.set_major_locator(MultipleLocator(1))\n",
        "plt.gca().xaxis.set_minor_locator(MultipleLocator(0.2))\n",
        "plt.xlim([-0.1, 1.1])\n",
        "plt.ylim([-0.1, 1.1])\n",
        "\n",
        "\n",
        "\n",
        "plt.subplot(gs1[2])\n",
        "plt.title('many steps of OCBC')\n",
        "plt.gca().set_aspect('equal')\n",
        "plt.xlabel('$\\pi(a = a_1)$', fontsize=14)\n",
        "\n",
        "\n",
        "for g in range(3):\n",
        "  z = np.eye(3)[g]\n",
        "  plt.plot([z[0]], [z[1]], marker='*', c=c_vec[g], markersize=20, alpha=0.5)\n",
        "\n",
        "\n",
        "policy_vec = []\n",
        "p_a_given_g = p_a_given_g_orig.copy()\n",
        "for _ in range(100):\n",
        "  policy_vec.append(p_a_given_g.copy())\n",
        "  p_a = np.sum(p_a_given_g * p_g[:, None], axis=0)\n",
        "  p_ag = p_g_given_a * p_a[None]\n",
        "  p_g_new = p_ag.sum(axis=1)\n",
        "  p_a_given_g_old = p_a_given_g\n",
        "  p_a_given_g = p_ag / p_g_new[:, None]  # OCBC\n",
        "\n",
        "policy_vec = np.array(policy_vec)\n",
        "cutoff = 3\n",
        "for g in range(3):\n",
        "  plt.plot(policy_vec[:cutoff+1, g, 0], policy_vec[:cutoff+1, g, 1], 'o', ms=5, c=c_vec[g])  \n",
        "  plt.plot(policy_vec[cutoff:, g, 0], policy_vec[cutoff:, g, 1], '--', ms=5, c=c_vec[g])  \n",
        "\n",
        "for i, (pi1, pi2) in enumerate(zip(policy_vec, policy_vec[1:])):\n",
        "  delta = 0.9 * (pi2 - pi1)\n",
        "  for g in range(3):\n",
        "    if i < cutoff:\n",
        "      plt.arrow(pi1[g, 0], pi1[g, 1], delta[g, 0], delta[g, 1], color=c_vec[g],\n",
        "                width=0.003, length_includes_head=True, head_width=0.02)\n",
        "\n",
        "\n",
        "plt.gca().yaxis.set_major_locator(MultipleLocator(1))\n",
        "plt.gca().yaxis.set_minor_locator(MultipleLocator(0.2))\n",
        "plt.gca().yaxis.set_major_formatter(FormatStrFormatter(''))\n",
        "plt.gca().xaxis.set_major_locator(MultipleLocator(1))\n",
        "plt.gca().xaxis.set_minor_locator(MultipleLocator(0.2))\n",
        "plt.xlim([-0.1, 1.1])\n",
        "plt.ylim([-0.1, 1.1])\n",
        "plt.fill_between([-2, 2], -2, 2, color=c_vec[3], alpha=0.2)\n",
        "\n",
        "plt.subplot(gs2[0])\n",
        "plt.title('normalized OCBC (ours)')\n",
        "plt.gca().set_aspect('equal')\n",
        "plt.xlabel('$\\pi(a = a_1)$', fontsize=14)\n",
        "\n",
        "for g in range(3):\n",
        "  z = np.eye(3)[g]\n",
        "  plt.plot([z[0]], [z[1]], marker='*', c=c_vec[g], markersize=20, alpha=0.5)\n",
        "\n",
        "policy_vec = []\n",
        "p_a_given_g = p_a_given_g_orig.copy()\n",
        "for _ in range(100):\n",
        "  policy_vec.append(p_a_given_g.copy())\n",
        "  p_a = np.sum(p_a_given_g * p_g[:, None], axis=0)\n",
        "  p_ag = p_g_given_a * p_a[None]\n",
        "  p_g_new = p_ag.sum(axis=1)\n",
        "  p_a_given_g_old = p_a_given_g.copy()\n",
        "  p_a_given_g = p_ag / p_g_new[:, None]  # OCBC\n",
        "  p_a_given_g = p_a_given_g / p_a[None] * p_a_given_g_old\n",
        "  p_a_given_g = p_a_given_g / np.sum(p_a_given_g, axis=1)[:, None]\n",
        "\n",
        "\n",
        "policy_vec = np.array(policy_vec)\n",
        "cutoff = 300\n",
        "for g in range(3):\n",
        "  plt.plot(policy_vec[:cutoff+1, g, 0], policy_vec[:cutoff+1, g, 1], 'o', ms=5, c=c_vec[g])  \n",
        "  plt.plot(policy_vec[cutoff:, g, 0], policy_vec[cutoff:, g, 1], '--', ms=5, c=c_vec[g])  \n",
        "\n",
        "for i, (pi1, pi2) in enumerate(zip(policy_vec, policy_vec[1:])):\n",
        "  delta = 0.9 * (pi2 - pi1)\n",
        "  for g in range(3):\n",
        "    if i < cutoff:\n",
        "      plt.arrow(pi1[g, 0], pi1[g, 1], delta[g, 0], delta[g, 1], color=c_vec[g],\n",
        "                width=0.003, length_includes_head=True, head_width=0.02)\n",
        "\n",
        "\n",
        "plt.gca().yaxis.set_major_locator(MultipleLocator(1))\n",
        "plt.gca().yaxis.set_minor_locator(MultipleLocator(0.2))\n",
        "plt.gca().yaxis.set_major_formatter(FormatStrFormatter(''))\n",
        "plt.gca().xaxis.set_major_locator(MultipleLocator(1))\n",
        "plt.gca().xaxis.set_minor_locator(MultipleLocator(0.2))\n",
        "plt.xlim([-0.1, 1.1])\n",
        "plt.ylim([-0.1, 1.1])\n",
        "plt.fill_between([-2, 2], -2, 2, color=c_vec[2], alpha=0.2)\n",
        "\n",
        "filename = 'fig_3.pdf'\n",
        "plt.savefig(filename, dpi=200, bbox_inches='tight')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "height": 273
        },
        "id": "yzf-g7Tr2-Ba",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1643236989243,
          "user_tz": 420,
          "elapsed": 3158,
          "user": {
          }
        },
        "outputId": "96acbbcd-b377-4f8a-e729-71aa5452ed00"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<a download='fig_3.pdf' id='id_862642747'>Download fig_3.pdf</a>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
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\");\n",
              "      const arr = new Uint8Array(chunk.length);\n",
              "      for(let i=0; i<chunk.length; ++i) {\n",
              "        arr[i] = chunk.charCodeAt(i);\n",
              "      }\n",
              "      window[\"id_862642748\"].push(arr);\n",
              "      return true;\n",
              "    })();\n",
              "    \n",
              "//# sourceURL=js_96c6500175"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "\n",
              "    (function() {\n",
              "      const blob = new Blob(window[\"id_862642748\"], {type: \"\"});\n",
              "      window[\"id_862642748\"] = URL.createObjectURL(blob);\n",
              "      return true;\n",
              "    })();\n",
              "  \n",
              "//# sourceURL=js_09707015d9"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "window[\"55c60a50-7ef9-11ec-a5f4-e78f1c3429d8\"] = document.getElementById(\"id_862642747\");\n",
              "//# sourceURL=js_346a368aea"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "window[\"55c63a48-7ef9-11ec-a5f4-e78f1c3429d8\"] = window[\"55c60a50-7ef9-11ec-a5f4-e78f1c3429d8\"].setAttribute(\"href\", id_862642748);\n",
              "//# sourceURL=js_f5dfa82efb"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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C+vXryc7OZunSpcTFxRULZdOmTVx11VW8/PLLTJgwodRwn332WV5//XW+/PJL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\nSUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 1250x400 with 4 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Relating OCBC to reward maximization [Fig. 2]"
      ],
      "metadata": {
        "id": "2RqM0YhuynDf"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "rc_params = {\n",
        "             'xtick.direction': 'inout',\n",
        "             'ytick.direction': 'inout',\n",
        "             'font.family': 'sans-serif',\n",
        "             'font.sans-serif': 'Roboto',\n",
        "             'legend.frameon': False,\n",
        "}\n",
        "matplotlib.rcParams.update(rc_params)\n",
        "\n",
        "fig = plt.figure(figsize=(8, 2.5))\n",
        "\n",
        "gs = gridspec.GridSpec(2, 3, hspace=0.05, wspace=0.02, height_ratios=(1, 2)) \n",
        "\n",
        "plt.subplot(gs[1, 0])\n",
        "t = np.linspace(0, 5, 1000)\n",
        "c_vec = plt.rcParams['axes.prop_cycle'].by_key()['color']\n",
        "p1 = scipy.stats.norm(loc=1.5, scale=0.5).pdf(t)\n",
        "p2 = scipy.stats.norm(loc=3, scale=0.5).pdf(t)\n",
        "plt.plot(t, p1, c=c_vec[0])\n",
        "plt.plot(t, p2, c=c_vec[1])\n",
        "plt.text(0.5, 0.5, '$e_1$', fontsize=16, ha='center', c=c_vec[0])\n",
        "plt.text(4, 0.5, '$e_2$', fontsize=16, ha='center', c=c_vec[1])\n",
        "plt.ylim([0, 1])\n",
        "plt.xlim([0, 5])\n",
        "plt.xticks(range(6), [])\n",
        "plt.yticks(np.linspace(0, 1, 6), [])\n",
        "plt.xlabel('actions', fontsize=10)\n",
        "plt.ylabel('action \\nprobabilties', fontsize=10, rotation=0, labelpad=27, ha='center', va='center')\n",
        "plt.text(0.2, 0.98, 'initial policies', fontsize=12, ha='left', va='top')\n",
        "plt.title('Step 1. Aggregate \\ndata from all tasks.', y=-0.3, ha='left', x=0.7,\n",
        "          va='top', fontsize=12, c=c_vec[2])\n",
        "\n",
        "\n",
        "plt.subplot(gs[0, 1])\n",
        "r1 = 5 - t\n",
        "r2 = t\n",
        "plt.plot(t, r1, c=c_vec[0])\n",
        "plt.plot(t, r2, c=c_vec[1])\n",
        "plt.text(0.3, 3., '$e_1$', fontsize=16, ha='left', c=c_vec[0])\n",
        "plt.text(4.7, 3., '$e_2$', fontsize=16, ha='right', c=c_vec[1])\n",
        "plt.yticks(plt.yticks()[0], [])\n",
        "plt.xlim(0, 5)\n",
        "plt.ylim([0, 5])\n",
        "plt.xticks(range(6), [])\n",
        "plt.ylabel('rewards', rotation=0, fontsize=10, ha='center', va='center', labelpad=17)\n",
        "\n",
        "plt.subplot(gs[1, 1])\n",
        "p_avg = (p1 + p2) / 2.0\n",
        "plt.plot(t, p_avg, c='k', alpha=0.5)\n",
        "plt.xlabel('actions', fontsize=10)\n",
        "plt.ylim([0, 1])\n",
        "plt.yticks(np.linspace(0, 1, 6), [])\n",
        "plt.text(0.2, 0.98, 'average\\n policy', fontsize=12, ha='left', va='top')\n",
        "plt.xlim([0, 5])\n",
        "plt.xticks(range(6), [])\n",
        "plt.text(2.5, 1, '$\\\\otimes$', fontsize=40, ha='center', va='center')\n",
        "\n",
        "\n",
        "print('Rewards of original policies: %.2f, %.2f' % (\n",
        "    p1 @ r1 / p1.sum(),\n",
        "    p2 @ r2 / p2.sum(),\n",
        "))\n",
        "plt.subplot(gs[1, 2])\n",
        "plt.title('Step 2. Reweight aggregate \\ndata by the task rewards.', y=-0.3, ha='left', x=-0.3,\n",
        "          va='top', fontsize=12, c=c_vec[2])\n",
        "p1 = (p_avg * r1) * p1.sum() / np.sum(p_avg * r1)\n",
        "plt.plot(t, p1, c=c_vec[0])\n",
        "\n",
        "p2 = (p_avg * r2) * p2.sum() / np.sum(p_avg * r2)\n",
        "plt.plot(t, p2, c=c_vec[1])\n",
        "plt.yticks([0.2, 0.4, 0.6, 0.8, 1.0], [])\n",
        "plt.ylim([0, 1])\n",
        "plt.text(0.2, 0.98, 'OCBC policies', fontsize=12, ha='left', va='top')\n",
        "plt.text(1, 0.6, '$e_1$', fontsize=16, ha='center', c=c_vec[0])\n",
        "plt.text(3.5, 0.6, '$e_2$', fontsize=16, ha='center', c=c_vec[1])\n",
        "plt.xlim([0, 5])\n",
        "plt.xticks(range(6), [])\n",
        "plt.xlabel('actions', fontsize=10)\n",
        "\n",
        "print('Rewards of new policies: %.2f, %.2f' % (\n",
        "    p1 @ r1 / p1.sum(),\n",
        "    p2 @ r2 / p2.sum(),\n",
        "))\n",
        "\n",
        "\n",
        "x = 205\n",
        "y = 90\n",
        "ar1 = matplotlib.patches.FancyArrowPatch(\n",
        "    (x, y), (x + 35, y),\n",
        "    fc = c_vec[2],\n",
        "    arrowstyle='simple',\n",
        "    mutation_scale = 40.,\n",
        "    linewidth=0\n",
        ")\n",
        "\n",
        "x = 355\n",
        "y = 90\n",
        "ar2 = matplotlib.patches.FancyArrowPatch(\n",
        "    (x, y), (x + 35, y),\n",
        "    arrowstyle='simple',\n",
        "    mutation_scale = 40.,\n",
        "    fc=c_vec[2], linewidth=0,\n",
        ")\n",
        "\n",
        "fig.patches.append(ar1)\n",
        "fig.patches.append(ar2)\n",
        "\n",
        "\n",
        "filename = 'fig_2.pdf'\n",
        "plt.savefig(filename, dpi=300, bbox_inches='tight')\n",
        "plt.show()\n",
        "\n"
      ],
      "metadata": {
        "colab": {
          "height": 267
        },
        "id": "qq8AW5EtRWVJ",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1643236990539,
          "user_tz": 420,
          "elapsed": 1163,
          "user": {
          }
        },
        "outputId": "708e4f4c-67f8-44af-9bef-a5f3591ad20f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Rewards of original policies: 3.50, 3.00\n",
            "Rewards of new policies: 3.04, 2.61\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ioqJE8+bNRXx8vDh37pzo2rVr0Qt/5cqVIiQkRGzdulVkZWWJJ554QvTo0cP6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            "text/plain": [
              "<Figure size 800x250 with 4 Axes>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<a download='fig_2.pdf' id='id_862642749'>Download fig_2.pdf</a>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
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              "\n",
              "    (function() {\n",
              "      window[\"id_862642750\"] = [];\n",
              "      const chunk = atob(\"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\");\n",
              "      const arr = new Uint8Array(chunk.length);\n",
              "      for(let i=0; i<chunk.length; ++i) {\n",
              "        arr[i] = chunk.charCodeAt(i);\n",
              "      }\n",
              "      window[\"id_862642750\"].push(arr);\n",
              "      return true;\n",
              "    })();\n",
              "    \n",
              "//# sourceURL=js_e04da28c85"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "\n",
              "    (function() {\n",
              "      const blob = new Blob(window[\"id_862642750\"], {type: \"\"});\n",
              "      window[\"id_862642750\"] = URL.createObjectURL(blob);\n",
              "      return true;\n",
              "    })();\n",
              "  \n",
              "//# sourceURL=js_382a9e9203"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "window[\"56eecb10-7ef9-11ec-a5f4-e78f1c3429d8\"] = document.getElementById(\"id_862642749\");\n",
              "//# sourceURL=js_947bbe3ee7"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "window[\"56eee762-7ef9-11ec-a5f4-e78f1c3429d8\"] = window[\"56eecb10-7ef9-11ec-a5f4-e78f1c3429d8\"].setAttribute(\"href\", id_862642750);\n",
              "//# sourceURL=js_29921d59b8"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### 2D navigation [Fig. 4]"
      ],
      "metadata": {
        "id": "Nw44gV-myAS0"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "height = 2\n",
        "width = 3\n",
        "num_s = height * width\n",
        "start_i, start_j = (1, 1)\n",
        "goals = [(0, 0),\n",
        "         (1, 2)]\n",
        "num_a = 4\n",
        "gamma = 0.9\n",
        "\n",
        "rc_params = {\n",
        "             'xtick.direction': 'inout',\n",
        "             'ytick.direction': 'inout',\n",
        "             'font.family': 'sans-serif',\n",
        "             'font.sans-serif': 'Roboto',\n",
        "             'legend.frameon': False,\n",
        "}\n",
        "matplotlib.rcParams.update(rc_params)\n",
        "c_vec = plt.rcParams['axes.prop_cycle'].by_key()['color']\n",
        "\n",
        "def step(s, a):\n",
        "  if np.random.random() < 0.5:\n",
        "    a = np.random.choice(4)\n",
        "  i, j = np.unravel_index(s, (height, width))\n",
        "  if a == 0:\n",
        "    i = max(0, i - 1)\n",
        "  elif a == 1:\n",
        "    j = min(width - 1, j + 1)\n",
        "  elif a == 2:\n",
        "    i = min(height - 1, i + 1)\n",
        "  else:\n",
        "    j = max(0, j - 1)\n",
        "  s = np.ravel_multi_index((i, j), (height, width))\n",
        "  return s\n",
        "\n",
        "num_episodes = 100\n",
        "def evaluate(pi):\n",
        "  max_episode_steps = 10\n",
        "  avg_time = []\n",
        "  for goal_i, goal_j in goals:\n",
        "    vec = []\n",
        "    for _ in range(num_episodes):\n",
        "      s = np.ravel_multi_index((start_i, start_j), (height, width))\n",
        "      g = np.ravel_multi_index((goal_i, goal_j), (height, width))\n",
        "      for t in range(max_episode_steps):\n",
        "        a = np.random.choice(num_a, p=pi[s, :, g])\n",
        "        s = step(s, a)\n",
        "        if s == g:\n",
        "          break\n",
        "      vec.append(t)\n",
        "    avg_time.append(np.mean(vec))\n",
        "  return avg_time\n",
        "\n",
        "\n",
        "data = {}\n",
        "for normalize in [True, False]:\n",
        "  print(normalize)\n",
        "  data[normalize] = []\n",
        "  for _ in tqdm.trange(10):\n",
        "    result_vec = []\n",
        "    pi_ocbc = np.ones((num_s, num_a, num_s)) / num_a\n",
        "\n",
        "    for iteration in range(20):\n",
        "      result_vec.append(evaluate(pi_ocbc))\n",
        "      counts = np.zeros((num_s, num_a, num_s)) + 0.01  # [s, a, ns]\n",
        "      for _ in range(num_episodes):\n",
        "        vec = []\n",
        "        s = np.ravel_multi_index((start_i, start_j), (height, width))\n",
        "        i = np.random.choice(2, p=[0.9, 0.1])  # p=[0.3, 0.3, 0.3, 0.1])\n",
        "        g = np.ravel_multi_index(goals[i], (height, width))\n",
        "        for _ in range(10):\n",
        "          a = np.random.choice(num_a, p=pi_ocbc[s, :, g])\n",
        "          vec.append((s, a))\n",
        "          s = step(s, a)\n",
        "        vec = np.array(vec)\n",
        "        for i in range(len(vec)):\n",
        "          for j in range(i, min(i + 20, len(vec))):\n",
        "            s1, a1 = vec[i]\n",
        "            s2, a2 = vec[j]\n",
        "            weight = gamma**(j - i)\n",
        "            counts[s1, a1, s2] += weight\n",
        "\n",
        "      pi_ocbc_old = pi_ocbc.copy()\n",
        "      p_sag = counts / counts.sum()\n",
        "      p_a_given_sg = p_sag / np.sum(p_sag, axis=1)[:, None, :]\n",
        "      \n",
        "      if normalize:\n",
        "        p_sa = p_sag.sum(axis=2)\n",
        "        p_a_given_s = p_sa / p_sa.sum(axis=1)[:, None]\n",
        "        Q = p_a_given_sg / p_a_given_s[:, :, None]\n",
        "        pi_ocbc = Q * pi_ocbc_old\n",
        "        pi_ocbc = pi_ocbc / pi_ocbc.sum(axis=1)[:, None, :]\n",
        "      else:\n",
        "        pi_ocbc = p_a_given_sg\n",
        "    data[normalize] = data[normalize] + [result_vec]"
      ],
      "metadata": {
        "id": "UXcld8_jvC6p",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1643239796915,
          "user_tz": 420,
          "elapsed": 43894,
          "user": {
          }
        },
        "outputId": "96fce97d-26eb-4e59-c697-4df46ea36f3c"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "True\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 10/10 [00:19<00:00,  1.97s/it]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "False\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "100%|██████████| 10/10 [00:24<00:00,  2.40s/it]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "### Compute the performance of the optimal policy.\n",
        "# We manually construct the optimal policy, and then evaluate it. This creates\n",
        "# the horizontal lines in the following plot.\n",
        "\n",
        "num_episodes = 10_000\n",
        "def evaluate(pi):\n",
        "  max_episode_steps = 10\n",
        "  avg_time = []\n",
        "  for goal_i, goal_j in goals:\n",
        "    vec = []\n",
        "    for _ in range(num_episodes):\n",
        "      s = np.ravel_multi_index((start_i, start_j), (height, width))\n",
        "      g = np.ravel_multi_index((goal_i, goal_j), (height, width))\n",
        "      for t in range(max_episode_steps):\n",
        "        a = np.random.choice(num_a, p=pi[s, :, g])\n",
        "        s = step(s, a)\n",
        "        if s == g:\n",
        "          break\n",
        "      vec.append(t)\n",
        "    avg_time.append(np.mean(vec))\n",
        "  return avg_time\n",
        "\n",
        "pi = np.zeros((num_s, num_a, num_s))\n",
        "for s in range(num_s):\n",
        "  s_i, s_j = np.unravel_index(s, (height, width))\n",
        "  for g in range(num_s):\n",
        "    g_i, g_j = np.unravel_index(g, (height, width))\n",
        "    if g_i < s_i:\n",
        "      a = 0\n",
        "    elif g_i > s_i:\n",
        "      a = 2\n",
        "    elif g_j < s_j:\n",
        "      a = 3\n",
        "    else:\n",
        "      a = 1\n",
        "    pi[s, a, g] = 1\n",
        "evaluate(pi)"
      ],
      "metadata": {
        "id": "kAgIB6pGr4M0",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1643237047200,
          "user_tz": 420,
          "elapsed": 3166,
          "user": {
          }
        },
        "outputId": "564ef4bd-8668-49c6-bd97-02222902b9d3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[2.7489, 1.2937]"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure(figsize=(6, 2))\n",
        "for col, key in enumerate([False, True]):\n",
        "  plt.subplot(1, 2, col + 1)\n",
        "  result_vec_vec = np.array(data[key])\n",
        "  for i in range(2):\n",
        "    vec_vec = [result_vec[:, i] for result_vec in result_vec_vec]\n",
        "    low, mid, high = np.quantile(vec_vec, [0.25, 0.5, 0.75], axis=0)\n",
        "    plt.errorbar(np.arange(len(low)), mid, yerr=(mid - low, high - mid), c=c_vec[i],\n",
        "                marker='o', markersize=4)\n",
        "    plt.plot([np.nan], [np.nan], '-o', c=c_vec[i],\n",
        "                 label='left goal' if i == 0 else 'right goal')\n",
        "    y = 2.7 if i == 0 else 1.2\n",
        "    plt.axhline(y, ls='--', linewidth=1, c=c_vec[i])\n",
        "    if col == 0:\n",
        "      plt.text(0, y, 'optimal policy', va='top', c=c_vec[i])\n",
        "  if col == 0:\n",
        "    plt.ylabel('steps to reach goal', fontsize=12)\n",
        "    plt.title('OCBC')\n",
        "  plt.gca().set_ylim([0, 7])\n",
        "  plt.gca().yaxis.set_major_locator(MultipleLocator(2))\n",
        "  plt.gca().yaxis.set_minor_locator(MultipleLocator(1))\n",
        "  plt.gca().xaxis.set_major_locator(MultipleLocator(5))\n",
        "  plt.gca().xaxis.set_minor_locator(MultipleLocator(1))\n",
        "  plt.grid(alpha=0.1)\n",
        "  if col == 1:\n",
        "    plt.gca().yaxis.set_major_formatter(FormatStrFormatter(''))\n",
        "    plt.title('Normalized OCBC (ours)')\n",
        "    plt.text(-5, -1.6, 'iterations', fontsize=14)\n",
        "    plt.legend(loc='upper right')\n",
        "\n",
        "plt.subplots_adjust(wspace=0)\n",
        "filename = 'fig_4.pdf'\n",
        "plt.savefig(filename, dpi=300, bbox_inches='tight')\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "height": 200
        },
        "id": "J5R9gTpVx7fc",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1643239839740,
          "user_tz": 420,
          "elapsed": 1080,
          "user": {
          }
        },
        "outputId": "d212d347-fb6c-47cd-b88c-8cc0017d20b1"
      },
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<a download='fig_4.pdf' id='id_862642761'>Download fig_4.pdf</a>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "\n",
              "    (function() {\n",
              "      window[\"id_862642762\"] = [];\n",
              "      const chunk = 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\");\n",
              "      const arr = new Uint8Array(chunk.length);\n",
              "      for(let i=0; i<chunk.length; ++i) {\n",
              "        arr[i] = chunk.charCodeAt(i);\n",
              "      }\n",
              "      window[\"id_862642762\"].push(arr);\n",
              "      return true;\n",
              "    })();\n",
              "    \n",
              "//# sourceURL=js_8e07fc6e0d"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "\n",
              "    (function() {\n",
              "      const blob = new Blob(window[\"id_862642762\"], {type: \"\"});\n",
              "      window[\"id_862642762\"] = URL.createObjectURL(blob);\n",
              "      return true;\n",
              "    })();\n",
              "  \n",
              "//# sourceURL=js_bde6f93611"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "window[\"f8868926-7eff-11ec-a5f4-e78f1c3429d8\"] = document.getElementById(\"id_862642761\");\n",
              "//# sourceURL=js_0ef19e5baf"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "window[\"f886a46a-7eff-11ec-a5f4-e78f1c3429d8\"] = window[\"f8868926-7eff-11ec-a5f4-e78f1c3429d8\"].setAttribute(\"href\", id_862642762);\n",
              "//# sourceURL=js_3675923cb2"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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5q3hCMbFrFgN/uF+nqtf4UyBP8eRdZGRkEPrbDPjyPrh1qfFZL8SU77bw7De/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\neYvFYqnFWCVvsVgstZj/B3Gz1xu/k/9uAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 600x200 with 2 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
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        ""
      ],
      "metadata": {
        "id": "vHVWxWS7ttYz"
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      "execution_count": null,
      "outputs": []
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}