path: root/rl/tutorials/08_cart_pole_q_learning.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-07T14:08:48.249166Z",
     "start_time": "2023-03-07T14:08:48.246325Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import gym\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import animation\n",
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-07T14:03:53.352738Z",
     "start_time": "2023-03-07T14:03:53.345794Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'0.15.4'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gym.version.VERSION"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-05T14:51:34.744085Z",
     "start_time": "2023-03-05T14:51:31.888070Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Looking in indexes: http://mirrors.aliyun.com/pypi/simple/\r\n",
      "Requirement already satisfied: JSAnimation in /Users/chunhuizhang/anaconda3/envs/py3/lib/python3.7/site-packages (0.1)\r\n"
     ]
    }
   ],
   "source": [
    "!pip install JSAnimation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-07T14:04:07.798088Z",
     "start_time": "2023-03-07T14:04:07.791365Z"
    }
   },
   "outputs": [],
   "source": [
    "from JSAnimation.IPython_display import display_animation\n",
    "from IPython.display import display, HTML"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 重新认识 cartpole 环境"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 小滑块/倒立摆\n",
    "- 典型的 mdp（markov decision process）\n",
    "    - 下一时刻的状态（转移）$s_{t+1}$ 只跟当前状态 $s_t$ 和（当前状态下采取的）$a_t$ 有关\n",
    "- action space is discrete and finite\n",
    "- state（observation）space is continuous"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-07T14:04:12.875444Z",
     "start_time": "2023-03-07T14:04:12.854714Z"
    }
   },
   "outputs": [],
   "source": [
    "env = gym.make('CartPole-v0')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### state/space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-07T14:04:15.382240Z",
     "start_time": "2023-03-07T14:04:15.377243Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-3.40156280e-02, -4.64929535e-05, -2.24331342e-02, -3.44344543e-02])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# init space\n",
    "env.reset()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-07T14:04:25.359650Z",
     "start_time": "2023-03-07T14:04:25.356727Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Discrete(2)\n"
     ]
    }
   ],
   "source": [
    "# action space\n",
    "print(env.action_space)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-07T14:04:30.487576Z",
     "start_time": "2023-03-07T14:04:30.484735Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n"
     ]
    }
   ],
   "source": [
    "print(env.action_space.n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-07T14:04:51.524995Z",
     "start_time": "2023-03-07T14:04:51.520685Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Box(4,)\n",
      "[-4.8000002e+00 -3.4028235e+38 -4.1887903e-01 -3.4028235e+38]\n",
      "[4.8000002e+00 3.4028235e+38 4.1887903e-01 3.4028235e+38]\n",
      "4\n"
     ]
    }
   ],
   "source": [
    "# observation space\n",
    "# https://www.gymlibrary.dev/environments/classic_control/cart_pole/\n",
    "print(env.observation_space)\n",
    "print(env.observation_space.low)\n",
    "print(env.observation_space.high)\n",
    "print(env.observation_space.shape[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### one episode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-05T14:57:32.225046Z",
     "start_time": "2023-03-05T14:57:31.832564Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step: 1, state: [-0.02012693  0.20925067  0.03958993 -0.29435305]\n",
      "step: 2, state: [-0.01594191  0.40378649  0.03370287 -0.57429172]\n",
      "step: 3, state: [-0.00786618  0.20820864  0.02221704 -0.27118479]\n",
      "step: 4, state: [-0.00370201  0.01277682  0.01679334  0.02842187]\n",
      "step: 5, state: [-0.00344647 -0.18258188  0.01736178  0.32635562]\n",
      "step: 6, state: [-0.00709811  0.01228863  0.02388889  0.03919801]\n",
      "step: 7, state: [-0.00685234 -0.18316759  0.02467285  0.33932136]\n",
      "step: 8, state: [-0.01051569 -0.37863177  0.03145928  0.63968147]\n",
      "step: 9, state: [-0.01808833 -0.18396223  0.04425291  0.35706915]\n",
      "step: 10, state: [-0.02176757 -0.37968447  0.05139429  0.66337121]\n",
      "step: 11, state: [-0.02936126 -0.18531377  0.06466172  0.38730339]\n",
      "step: 12, state: [-0.03306753  0.00883356  0.07240779  0.1156883 ]\n",
      "step: 13, state: [-0.03289086 -0.18724716  0.07472155  0.43030799]\n",
      "step: 14, state: [-0.03663581  0.00674154  0.08332771  0.16208459]\n",
      "step: 15, state: [-0.03650098 -0.18946834  0.0865694   0.47984822]\n",
      "step: 16, state: [-0.04029034 -0.38569887  0.09616637  0.79851137]\n",
      "step: 17, state: [-0.04800432 -0.19201853  0.11213659  0.53756254]\n",
      "step: 18, state: [-0.05184469  0.00136303  0.12288785  0.28221117]\n",
      "step: 19, state: [-0.05181743  0.19453743  0.12853207  0.0306729 ]\n",
      "step: 20, state: [-0.04792668  0.38760429  0.12914553 -0.21885405]\n",
      "step: 21, state: [-0.0401746   0.19089548  0.12476845  0.1116153 ]\n",
      "step: 22, state: [-0.03635669 -0.00577295  0.12700075  0.44091157]\n",
      "step: 23, state: [-0.03647215 -0.20244188  0.13581898  0.770777  ]\n",
      "step: 24, state: [-0.04052098 -0.00942435  0.15123452  0.52372515]\n",
      "step: 25, state: [-0.04070947 -0.20631499  0.16170903  0.85998375]\n",
      "step: 26, state: [-0.04483577 -0.0137211   0.1789087   0.62219743]\n",
      "step: 27, state: [-0.04511019  0.17851121  0.19135265  0.39077045]\n",
      "step: 28, state: [-0.04153997 -0.01873813  0.19916806  0.73715912]\n",
      "step: 29, state: [-0.04191473  0.17315764  0.21391124  0.51317475]\n"
     ]
    }
   ],
   "source": [
    "env = gym.make('CartPole-v0')\n",
    "# observation = env.reset()\n",
    "state = env.reset()\n",
    "steps = 0\n",
    "frames = []\n",
    "while True:\n",
    "    frames.append(env.render(mode='rgb_array'))\n",
    "    action = env.action_space.sample()\n",
    "    state, reward, done, info = env.step(action)\n",
    "    steps += 1\n",
    "    print(f'step: {steps}, state: {state}')\n",
    "    if done:\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-05T14:58:23.485976Z",
     "start_time": "2023-03-05T14:58:23.446404Z"
    }
   },
   "outputs": [
    {
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       "        [[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]]], dtype=uint8),\n",
       " array([[[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
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       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255]]], dtype=uint8),\n",
       " array([[[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255]]], dtype=uint8),\n",
       " array([[[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255]]], dtype=uint8),\n",
       " array([[[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
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       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255]]], dtype=uint8),\n",
       " array([[[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255]]], dtype=uint8),\n",
       " array([[[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
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       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255]]], dtype=uint8),\n",
       " array([[[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255]]], dtype=uint8),\n",
       " array([[[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255]]], dtype=uint8),\n",
       " array([[[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
       "        ...,\n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255]]], dtype=uint8),\n",
       " array([[[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
       "        ...,\n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255]]], dtype=uint8),\n",
       " array([[[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
       "        ...,\n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255]]], dtype=uint8),\n",
       " array([[[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       " \n",
       "        [[255, 255, 255],\n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
       "        ...,\n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255]]], dtype=uint8),\n",
       " array([[[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
       "        ...,\n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]]], dtype=uint8),\n",
       " array([[[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
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       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
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       "         [255, 255, 255],\n",
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       "         [255, 255, 255]],\n",
       " \n",
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       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255]]], dtype=uint8),\n",
       " array([[[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       " \n",
       "        ...,\n",
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       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
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       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255]]], dtype=uint8),\n",
       " array([[[255, 255, 255],\n",
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       "         ...,\n",
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       " \n",
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       "         ...,\n",
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       " \n",
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       "         ...,\n",
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       " \n",
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       " \n",
       "        [[255, 255, 255],\n",
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       "         ...,\n",
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       " \n",
       "        [[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
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       "         [255, 255, 255],\n",
       "         [255, 255, 255]]], dtype=uint8),\n",
       " array([[[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
       "        ...,\n",
       " \n",
       "        [[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]]], dtype=uint8),\n",
       " array([[[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
       "        ...,\n",
       " \n",
       "        [[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]]], dtype=uint8),\n",
       " array([[[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
       "        ...,\n",
       " \n",
       "        [[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]]], dtype=uint8),\n",
       " array([[[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
       "        ...,\n",
       " \n",
       "        [[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]],\n",
       " \n",
       "        [[255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         ...,\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255],\n",
       "         [255, 255, 255]]], dtype=uint8)]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frames"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-07T14:05:15.008732Z",
     "start_time": "2023-03-07T14:05:15.003533Z"
    }
   },
   "outputs": [],
   "source": [
    "def display_frames_as_gif(frames, output):\n",
    "    \"\"\"\n",
    "    Displays a list of frames as a gif, with controls\n",
    "    以gif格式显示关键帧列，带有控件\n",
    "    \"\"\"\n",
    "    \n",
    "    fig = plt.figure(figsize=(frames[0].shape[1]/72.0, frames[0].shape[0]/72.0),dpi=72)\n",
    "    patch = plt.imshow(frames[0])\n",
    "    plt.axis('off')\n",
    "    \n",
    "    def animate(i):\n",
    "        img = patch.set_data(frames[i])\n",
    "        return img   ## *** return是必须要有的 ***\n",
    "        \n",
    "    anim = animation.FuncAnimation(plt.gcf(), animate, frames=len(frames), interval=50)\n",
    "    \n",
    "    anim.save(output)\n",
    "    return HTML(anim.to_jshtml())  ## *** 返回一个HTML对象，以便被调用者显示。 ***\n",
    "    # display(display_animation(anim, default_mode='loop'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-05T14:59:09.169623Z",
     "start_time": "2023-03-05T14:58:48.224146Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<link rel=\"stylesheet\"\n",
       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/css/font-awesome.min.css\">\n",
       "<script language=\"javascript\">\n",
       "  function isInternetExplorer() {\n",
       "    ua = navigator.userAgent;\n",
       "    /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
       "    return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
       "  }\n",
       "\n",
       "  /* Define the Animation class */\n",
       "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
       "    this.img_id = img_id;\n",
       "    this.slider_id = slider_id;\n",
       "    this.loop_select_id = loop_select_id;\n",
       "    this.interval = interval;\n",
       "    this.current_frame = 0;\n",
       "    this.direction = 0;\n",
       "    this.timer = null;\n",
       "    this.frames = new Array(frames.length);\n",
       "\n",
       "    for (var i=0; i<frames.length; i++)\n",
       "    {\n",
       "     this.frames[i] = new Image();\n",
       "     this.frames[i].src = frames[i];\n",
       "    }\n",
       "    var slider = document.getElementById(this.slider_id);\n",
       "    slider.max = this.frames.length - 1;\n",
       "    if (isInternetExplorer()) {\n",
       "        // switch from oninput to onchange because IE <= 11 does not conform\n",
       "        // with W3C specification. It ignores oninput and onchange behaves\n",
       "        // like oninput. In contrast, Microsoft Edge behaves correctly.\n",
       "        slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
       "        slider.setAttribute('oninput', null);\n",
       "    }\n",
       "    this.set_frame(this.current_frame);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.get_loop_state = function(){\n",
       "    var button_group = document[this.loop_select_id].state;\n",
       "    for (var i = 0; i < button_group.length; i++) {\n",
       "        var button = button_group[i];\n",
       "        if (button.checked) {\n",
       "            return button.value;\n",
       "        }\n",
       "    }\n",
       "    return undefined;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.set_frame = function(frame){\n",
       "    this.current_frame = frame;\n",
       "    document.getElementById(this.img_id).src =\n",
       "            this.frames[this.current_frame].src;\n",
       "    document.getElementById(this.slider_id).value = this.current_frame;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.next_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.previous_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.first_frame = function()\n",
       "  {\n",
       "    this.set_frame(0);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.last_frame = function()\n",
       "  {\n",
       "    this.set_frame(this.frames.length - 1);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.slower = function()\n",
       "  {\n",
       "    this.interval /= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.faster = function()\n",
       "  {\n",
       "    this.interval *= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_forward = function()\n",
       "  {\n",
       "    this.current_frame += 1;\n",
       "    if(this.current_frame < this.frames.length){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.first_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.last_frame();\n",
       "        this.reverse_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.last_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_reverse = function()\n",
       "  {\n",
       "    this.current_frame -= 1;\n",
       "    if(this.current_frame >= 0){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.last_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.first_frame();\n",
       "        this.play_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.first_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.pause_animation = function()\n",
       "  {\n",
       "    this.direction = 0;\n",
       "    if (this.timer){\n",
       "      clearInterval(this.timer);\n",
       "      this.timer = null;\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.play_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = 1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_forward();\n",
       "    }, this.interval);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.reverse_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = -1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_reverse();\n",
       "    }, this.interval);\n",
       "  }\n",
       "</script>\n",
       "\n",
       "<style>\n",
       ".animation {\n",
       "    display: inline-block;\n",
       "    text-align: center;\n",
       "}\n",
       "input[type=range].anim-slider {\n",
       "    width: 374px;\n",
       "    margin-left: auto;\n",
       "    margin-right: auto;\n",
       "}\n",
       ".anim-buttons {\n",
       "    margin: 8px 0px;\n",
       "}\n",
       ".anim-buttons button {\n",
       "    padding: 0;\n",
       "    width: 36px;\n",
       "}\n",
       ".anim-state label {\n",
       "    margin-right: 8px;\n",
       "}\n",
       ".anim-state input {\n",
       "    margin: 0;\n",
       "    vertical-align: middle;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<div class=\"animation\">\n",
       "  <img id=\"_anim_img2df701fd018149c4a11e47e89b9e0a44\">\n",
       "  <div class=\"anim-controls\">\n",
       "    <input id=\"_anim_slider2df701fd018149c4a11e47e89b9e0a44\" type=\"range\" class=\"anim-slider\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           oninput=\"anim2df701fd018149c4a11e47e89b9e0a44.set_frame(parseInt(this.value));\"></input>\n",
       "    <div class=\"anim-buttons\">\n",
       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"anim2df701fd018149c4a11e47e89b9e0a44.slower()\">\n",
       "          <i class=\"fa fa-minus\"></i></button>\n",
       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"anim2df701fd018149c4a11e47e89b9e0a44.first_frame()\">\n",
       "        <i class=\"fa fa-fast-backward\"></i></button>\n",
       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"anim2df701fd018149c4a11e47e89b9e0a44.previous_frame()\">\n",
       "          <i class=\"fa fa-step-backward\"></i></button>\n",
       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"anim2df701fd018149c4a11e47e89b9e0a44.reverse_animation()\">\n",
       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"anim2df701fd018149c4a11e47e89b9e0a44.pause_animation()\">\n",
       "          <i class=\"fa fa-pause\"></i></button>\n",
       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"anim2df701fd018149c4a11e47e89b9e0a44.play_animation()\">\n",
       "          <i class=\"fa fa-play\"></i></button>\n",
       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"anim2df701fd018149c4a11e47e89b9e0a44.next_frame()\">\n",
       "          <i class=\"fa fa-step-forward\"></i></button>\n",
       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"anim2df701fd018149c4a11e47e89b9e0a44.last_frame()\">\n",
       "          <i class=\"fa fa-fast-forward\"></i></button>\n",
       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"anim2df701fd018149c4a11e47e89b9e0a44.faster()\">\n",
       "          <i class=\"fa fa-plus\"></i></button>\n",
       "    </div>\n",
       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_select2df701fd018149c4a11e47e89b9e0a44\"\n",
       "          class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_2df701fd018149c4a11e47e89b9e0a44\"\n",
       "             >\n",
       "      <label for=\"_anim_radio1_2df701fd018149c4a11e47e89b9e0a44\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_2df701fd018149c4a11e47e89b9e0a44\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio2_2df701fd018149c4a11e47e89b9e0a44\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_2df701fd018149c4a11e47e89b9e0a44\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_2df701fd018149c4a11e47e89b9e0a44\">Reflect</label>\n",
       "    </form>\n",
       "  </div>\n",
       "</div>\n",
       "\n",
       "\n",
       "<script language=\"javascript\">\n",
       "  /* Instantiate the Animation class. */\n",
       "  /* The IDs given should match those used in the template above. */\n",
       "  (function() {\n",
       "    var img_id = \"_anim_img2df701fd018149c4a11e47e89b9e0a44\";\n",
       "    var slider_id = \"_anim_slider2df701fd018149c4a11e47e89b9e0a44\";\n",
       "    var loop_select_id = \"_anim_loop_select2df701fd018149c4a11e47e89b9e0a44\";\n",
       "    var frames = new Array(29);\n",
       "    \n",
       "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAABLAAAAMgCAYAAAAz4JsCAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
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       "QmCC\\\n",
       "\"\n",
       "\n",
       "\n",
       "    /* set a timeout to make sure all the above elements are created before\n",
       "       the object is initialized. */\n",
       "    setTimeout(function() {\n",
       "        anim2df701fd018149c4a11e47e89b9e0a44 = new Animation(frames, img_id, slider_id, 50.0,\n",
       "                                 loop_select_id);\n",
       "    }, 0);\n",
       "  })()\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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AnhCYAHAeu//za1G3W6VnAEDfE5gAcB6n3jrS8dm1l2yNRnM0cQ0A9C+BCQBddNmNd0VzbKL0DADoCYEJAOfQXlqMum6XngEAA0FgAsA5HHji3+Pkm7tLzwCAgSAwAeAc6rru+OzkpdtiYmZL4hoA6G8CEwC6ZO3GLbFmw6WlZwBAzwhMADiLpfkTcer4wdIzAGBgCEwAOIuTh/bE4Rd+UnoGAAwMgQkAXTA2NROX3vjx0jMAoKcEJgB0QdUcjfHpjaVnAEBPCUwAeAft1lIc3vVw6RkAMFAEJgC8g7rdikO7Hun4fNVoJq4BgMEgMAGgC979iT8tPQEAek5gAkAXuIMJwDASmADwDvb++L6Iul16BgAMFIEJAO/g5MFXOz47vm6TO5gADCWBCQDJttz+6WiOTZSeAQA9JzAB4FfUdTsi6tIzAGDgCEwA+BWvPfrtOHloT+kZADBwBCYA/Iq6vRRRd3YHc2LjlTG+7pLkRQAwGAQmACSavvzamJi5ovQMAChCYALA27QW52Np/q3SMwBgIAlMAHibtw68GIee+5/SMwBgIAlMAEgyNjUTG6/7QOkZAFCMwASAJI3RNbF245bSMwCgGIEJAKe1W0sxu+fp0jMAYGAJTAA4rW4txhs7H+r4fFVViWsAYPAITABIUcW2u75UegQAFCUwASDJyJrJ0hMAoCiBCQCn7X/8OxF1XXoGAAwsgQkAp83ufabjs7+4e+k9mAAMN4EJAAm2fuRz0RxbU3oGABQlMAEghbuXACAwASB+8f7L+aMHSs8AgIEmMAEgIpbmT0TdbnV0dnz9pTG6dl3yIgAYPAITAC7QhqvfG2svvqr0DAAoTmACMPTaraVotxZLzwCAgScwARh6s3ufiYM//0HpGQAw8AQmAFyA0cmLYsPWm0rPAIC+IDAB4AKMTkzH1GXbS88AgL4gMAEYau3WUpx8c3fpGQCwKghMAIZae2kh9j/+ndIzAGBVEJgA0Kmqiqs/9NnSKwCgbwhMAOhYFePrN5UeAQB9Q2ACMNTefOa/Sk8AgFVDYAIw1A7veqTjs43mSOISABh8AhMAOnTNx/44GiNjpWcAQN8QmADQoapqRFVVpWcAQN8QmAAMrdef/H4sHD9UegYArBoCE4ChtTB7MOrWYkdnRycviub4RPIiABhsAhMAOrDx2ttj8pKtpWcAQF8RmAAMpbpuR123S88AgFVFYAIwlI698mQcfPaHpWcAwKoiMAEYSnW7HdHhHczRtetj6vJrkxcBwOATmACwQmNTM7H+yhtKzwCAviMwARg6dbsVC8cPlp4BAKuOwARg6CwtnIx9j/xz6RkAsOoITABYiaoRm2/5ZOkVANCXBCYArEBVVTF16TWlZwBAXxKYAAydIy89VnoCAKxKAhOAofPGUw+UngAAq5LABIAVuOZjX4yqOVp6BgD0JYEJACvQHJ2IqqpKzwCAvlTVdX2u6+e8CAAr9dhjj8VXvvKVYr//7g9eH9dNHon20kJH57/+6PHYc3QpedXZffWrX42rrrqqZ78PAJbhrP/TOtLLFQCwf//+uO+++4r9/nePfzCu/eD1HZ2dPbEQ//H9B2Ln7jeTV53dl7/85Z79LgC4UF4iCwDL9E8PPt3TuASAQeMOJgBD7Z3eKeItlgDQGYEJwND40Huvjt+5dXvUdcR8ezIiIh4/cmfMtabPPGbD2Otxw7ofx3hjLhpVu9RUABhIAhOAoTE+1oyJ8dHYe/LaeOLYR07/7f+/XXlg/po4MP+uuG76p7F98okzdzMPz87Frr2HejkXAAaO92ACMFT2nHx3PD37gfhFWJ7ttbBVPH/85njxxI1n/uaV14/GQ0/s7sFCABhc7mACMBSqKmKucW08Pfub0arHzvv4Ohrx/PH3Rx1VbJt8sgcLAWDwuYMJwFDYMD0df/iZP1hWXP5SO0biueO3xNHFi7u4DABWD4EJwFBYbI/Fyyd2dHCyilarHfc+8FT6JgBYbQQmAJzHfGs0fvTUq6VnAEDfE5gADIWbr9vc8dnHjtwV7WgmrgGA1UlgAjAU/uSTt575ypGV2rr26ajCd2ICwPkITAA4j7/+xt/HUqtVegYA9D2BCcBQaFStWD9ycMXnJptH4+CRlZ8DgGEkMAFY9e66ZVtsnIrYNvWzFZ/dMrErpkaO5o8CgFVIYAKw6t3+61tiamIsLhnfG1es2RUR9TJO1bFx7LW4bGxntNvLeTwAMFJ6AAB024v7DsePd+6JjevWxk1bHoo4GrFvfntEnP1TfzaO7Y/bZu6Pv/n2T2Ln7jd7thUABpnABGDVu/eBp+LeB56KrZdtiA+99+po1Y/G7pM3xIdv3BpTl90Vp9oTZx472TwaV659LrZMPB+Nqh117e4lACyXwARgaOw+cDR2Hzh6+qfH48WfT8XImm+c+Y7LP/vsh2PrpWtisnks6qWIVtWMxZavJwGA5RKYAAytA4ffiojnz/z8pT9/9syLZsdGm/GFT7w//vF7K/9gIAAYVgITAE57+4f5zC0sxV9865GCawBg8JwzMO+4445e7QBgSBw86DslV+Lzn/98TE1NlZ4BAGc8+OCDZ71WnevDCxYWFnyyAQCp7r///rj77rtLzxgYjz76aOzYsaP0DAA4Y3x8/Kwfw37OO5jj4+P5awAYaqOjo6UnDJSxsTHPxwAMjEbpAQAAAKwOAhMAAIAUAhMAAIAUAhMAAIAUAhMAAIAUAhMAAIAUAhMAAIAUAhMAAIAUAhMAAIAUAhMAAIAUAhMAAIAUAhMAAIAUAhMAAIAUAhMAAIAUAhMAAIAUAhMAAIAUAhMAAIAUAhMAAIAUAhMAAIAUAhMAAIAUI6UHADBcNm/eHPfcc0/pGQNj/fr1pScAwLJVdV2f6/o5LwIAADB0qrNd8BJZAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUghMAAAAUoyc53rVkxUAAAAMPHcwAQAASCEwAQAASCEwAQAASCEwAQAASCEwAQAASCEwAQAASPG/e2QgBt5rhWsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1200x800 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1200x800 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "display_frames_as_gif(frames, output='./save/rand_cartpole.gif')\n",
    "display_frames_as_gif(frames, output='./save/rand_cartpole.mp4')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 状态离散化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-05T15:01:26.306200Z",
     "start_time": "2023-03-05T15:01:26.301178Z"
    }
   },
   "outputs": [],
   "source": [
    "NUM_DIGITIZED = 6\n",
    "\n",
    "# 分桶， 5个值，对应 6 个分段，即 6 个桶 (0, 1, 2, 3, 4, 5)\n",
    "def bins(clip_min, clip_max, num_bins=NUM_DIGITIZED):\n",
    "    return np.linspace(clip_min, clip_max, num_bins+1)[1:-1]\n",
    "\n",
    "# 按 6 进制映射将 4位 6 进制数映射为 id，\n",
    "def digitize_state(observation):\n",
    "    pos, cart_v, angle, pole_v = observation\n",
    "    digitized = [np.digitize(pos, bins=bins(-2.4, 2.4, NUM_DIGITIZED)), \n",
    "                 np.digitize(cart_v, bins=bins(-3., 3, NUM_DIGITIZED)), \n",
    "                 np.digitize(angle, bins=bins(-0.418, 0.418, NUM_DIGITIZED)), \n",
    "                 np.digitize(pole_v, bins=bins(-2, 2, NUM_DIGITIZED))]\n",
    "    # 3,1,2,4 (4位10进制数) = 4*10^0 + 2*10^1 + 1*10^2 + 3*10^3，最终的取值范围是 0-9999，总计 10^4 == 10000\n",
    "    # a,b,c,d (4位6进制数) = d*6^0 + c*6^1 + b*6^2 + a*6^3，最终的取值范围是 0-`5555`(1295)，总计 6^4 == 1296\n",
    "    ind = sum([d*(NUM_DIGITIZED**i) for i, d in enumerate(digitized)])\n",
    "    return ind\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-05T15:01:29.874797Z",
     "start_time": "2023-03-05T15:01:29.871656Z"
    }
   },
   "outputs": [],
   "source": [
    "obs = env.reset()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-05T15:01:31.165281Z",
     "start_time": "2023-03-05T15:01:31.161059Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.04002152,  0.00259074, -0.03391407, -0.04418303])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "obs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-05T14:25:41.628539Z",
     "start_time": "2023-03-05T14:25:41.625136Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.6, -0.8,  0. ,  0.8,  1.6])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bins(-2.4, 2.4, NUM_DIGITIZED)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## q-learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-07T14:21:15.848998Z",
     "start_time": "2023-03-07T14:21:15.838895Z"
    }
   },
   "outputs": [],
   "source": [
    "class Agent:\n",
    "    def __init__(self, action_space, n_states, eta=0.5, gamma=0.99, NUM_DIGITIZED=6):\n",
    "        self.eta = 0.5\n",
    "        self.gamme = gamma\n",
    "        # Discrete(2)\n",
    "        self.action_space = action_space\n",
    "        self.NUM_DIGITIZED = NUM_DIGITIZED\n",
    "        self.q_table = np.random.uniform(0, 1, size=(NUM_DIGITIZED**n_states, self.action_space.n))\n",
    "        \n",
    "    # 分桶， 5个值，对应 6 个分段，即 6 个桶 (0, 1, 2, 3, 4, 5)\n",
    "    @staticmethod\n",
    "    def _bins(clip_min, clip_max, num_bins):\n",
    "        return np.linspace(clip_min, clip_max, num_bins+1)[1:-1]\n",
    "\n",
    "    # 按 6 进制映射将 4位 6 进制数映射为 id，\n",
    "    @staticmethod\n",
    "    def _digitize_state(observation, NUM_DIGITIZED):\n",
    "        pos, cart_v, angle, pole_v = observation\n",
    "        digitized = [np.digitize(pos, bins=Agent._bins(-2.4, 2.4, NUM_DIGITIZED)), \n",
    "                     np.digitize(cart_v, bins=Agent._bins(-3., 3, NUM_DIGITIZED)), \n",
    "                     np.digitize(angle, bins=Agent._bins(-0.418, 0.418, NUM_DIGITIZED)), \n",
    "                     np.digitize(pole_v, bins=Agent._bins(-2, 2, NUM_DIGITIZED))]\n",
    "        # 3,1,2,4 (4位10进制数) = 4*10^0 + 2*10^1 + 1*10^2 + 3*10^3，最终的取值范围是 0-9999，总计 10^4 == 10000\n",
    "        # a,b,c,d (4位6进制数) = d*6^0 + c*6^1 + b*6^2 + a*6^3，最终的取值范围是 0-`5555`(1295)，总计 6^4 == 1296\n",
    "        ind = sum([d*(NUM_DIGITIZED**i) for i, d in enumerate(digitized)])\n",
    "        return ind\n",
    "\n",
    "#     def update_q_table()\n",
    "    def q_learning(self, obs, action, reward, obs_next):\n",
    "        obs_ind = Agent._digitize_state(obs, self.NUM_DIGITIZED)\n",
    "        obs_next_ind = Agent._digitize_state(obs_next, self.NUM_DIGITIZED)\n",
    "        self.q_table[obs_ind, action] = self.q_table[obs_ind, action] + self.eta*(reward + max(self.q_table[obs_next_ind, :]) - self.q_table[obs_ind, action])\n",
    "        \n",
    "    def choose_action(self, state, episode):\n",
    "        eps = 0.5*1/(episode + 1)\n",
    "        state_ind = Agent._digitize_state(state, self.NUM_DIGITIZED)\n",
    "        # epsilon greedy\n",
    "        if random.random() < eps:\n",
    "            action = self.action_space.sample()\n",
    "        else:\n",
    "            action = np.argmax(self.q_table[state_ind, :])\n",
    "        return action"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-07T14:25:28.552642Z",
     "start_time": "2023-03-07T14:25:15.162622Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "episode: 0, finish 15 time steps.\n",
      "episode: 1, finish 9 time steps.\n",
      "episode: 2, finish 44 time steps.\n",
      "episode: 3, finish 21 time steps.\n",
      "episode: 4, finish 14 time steps.\n",
      "episode: 5, finish 79 time steps.\n",
      "episode: 6, finish 45 time steps.\n",
      "episode: 7, finish 8 time steps.\n",
      "episode: 8, finish 12 time steps.\n",
      "episode: 9, finish 26 time steps.\n",
      "episode: 10, finish 71 time steps.\n",
      "episode: 11, finish 91 time steps.\n",
      "episode: 12, finish 66 time steps.\n",
      "episode: 13, finish 40 time steps.\n",
      "episode: 14, finish 57 time steps.\n",
      "episode: 15, finish 14 time steps.\n",
      "episode: 16, finish 9 time steps.\n",
      "episode: 17, finish 125 time steps.\n",
      "episode: 18, finish 9 time steps.\n",
      "episode: 19, finish 22 time steps.\n",
      "episode: 20, finish 30 time steps.\n",
      "episode: 21, finish 54 time steps.\n",
      "episode: 22, finish 34 time steps.\n",
      "episode: 23, finish 37 time steps.\n",
      "episode: 24, finish 12 time steps.\n",
      "episode: 25, finish 8 time steps.\n",
      "episode: 26, finish 53 time steps.\n",
      "episode: 27, finish 9 time steps.\n",
      "episode: 28, finish 95 time steps.\n",
      "episode: 29, finish 48 time steps.\n",
      "episode: 30, finish 23 time steps.\n",
      "episode: 31, finish 12 time steps.\n",
      "episode: 32, finish 84 time steps.\n",
      "episode: 33, finish 10 time steps.\n",
      "episode: 34, finish 63 time steps.\n",
      "episode: 35, finish 23 time steps.\n",
      "episode: 36, finish 85 time steps.\n",
      "episode: 37, finish 10 time steps.\n",
      "episode: 38, finish 73 time steps.\n",
      "episode: 39, finish 100 time steps.\n",
      "episode: 40, finish 81 time steps.\n",
      "episode: 41, finish 68 time steps.\n",
      "episode: 42, finish 92 time steps.\n",
      "episode: 43, finish 129 time steps.\n",
      "episode: 44, finish 15 time steps.\n",
      "episode: 45, finish 96 time steps.\n",
      "episode: 46, finish 10 time steps.\n",
      "episode: 47, finish 7 time steps.\n",
      "episode: 48, finish 7 time steps.\n",
      "episode: 49, finish 9 time steps.\n",
      "episode: 50, finish 38 time steps.\n",
      "episode: 51, finish 85 time steps.\n",
      "episode: 52, finish 90 time steps.\n",
      "episode: 53, finish 18 time steps.\n",
      "episode: 54, finish 80 time steps.\n",
      "episode: 55, finish 104 time steps.\n",
      "episode: 56, finish 156 time steps.\n",
      "episode: 57, finish 183 time steps.\n",
      "episode: 58, finish 25 time steps.\n",
      "episode: 59, finish 121 time steps.\n",
      "episode: 60, finish 122 time steps.\n",
      "episode: 61, finish 112 time steps.\n",
      "episode: 62, finish 19 time steps.\n",
      "episode: 63, finish 56 time steps.\n",
      "episode: 64, finish 183 time steps.\n",
      "episode: 65, finish 35 time steps.\n",
      "episode: 66, finish 23 time steps.\n",
      "episode: 67, finish 146 time steps.\n",
      "episode: 68, finish 58 time steps.\n",
      "episode: 69, finish 114 time steps.\n",
      "episode: 70, finish 39 time steps.\n",
      "episode: 71, finish 107 time steps.\n",
      "episode: 72, finish 58 time steps.\n",
      "episode: 73, finish 189 time steps.\n",
      "episode: 74, finish 27 time steps.\n",
      "episode: 75, finish 106 time steps.\n",
      "episode: 76, finish 102 time steps.\n",
      "episode: 77, finish 109 time steps.\n",
      "episode: 78, finish 48 time steps.\n",
      "episode: 79, finish 85 time steps.\n",
      "episode: 80, finish 82 time steps.\n",
      "episode: 81, finish 90 time steps.\n",
      "episode: 82, finish 199 time steps.\n",
      "episode: 83, finish 10 time steps.\n",
      "episode: 84, finish 120 time steps.\n",
      "episode: 85, finish 59 time steps.\n",
      "episode: 86, finish 168 time steps.\n",
      "episode: 87, finish 199 time steps.\n",
      "episode: 88, finish 166 time steps.\n",
      "episode: 89, finish 199 time steps.\n",
      "episode: 90, finish 43 time steps.\n",
      "episode: 91, finish 131 time steps.\n",
      "episode: 92, finish 54 time steps.\n",
      "episode: 93, finish 191 time steps.\n",
      "episode: 94, finish 199 time steps.\n",
      "episode: 95, finish 71 time steps.\n",
      "episode: 96, finish 199 time steps.\n",
      "episode: 97, finish 167 time steps.\n",
      "episode: 98, finish 199 time steps.\n",
      "episode: 99, finish 102 time steps.\n",
      "episode: 100, finish 27 time steps.\n",
      "episode: 101, finish 184 time steps.\n",
      "episode: 102, finish 122 time steps.\n",
      "episode: 103, finish 166 time steps.\n",
      "episode: 104, finish 120 time steps.\n",
      "episode: 105, finish 39 time steps.\n",
      "episode: 106, finish 116 time steps.\n",
      "episode: 107, finish 155 time steps.\n",
      "episode: 108, finish 109 time steps.\n",
      "episode: 109, finish 199 time steps.\n",
      "episode: 110, finish 31 time steps.\n",
      "episode: 111, finish 199 time steps.\n",
      "episode: 112, finish 152 time steps.\n",
      "episode: 113, finish 199 time steps.\n",
      "episode: 114, finish 117 time steps.\n",
      "episode: 115, finish 95 time steps.\n",
      "episode: 116, finish 165 time steps.\n",
      "episode: 117, finish 143 time steps.\n",
      "episode: 118, finish 32 time steps.\n",
      "episode: 119, finish 9 time steps.\n",
      "episode: 120, finish 55 time steps.\n",
      "episode: 121, finish 177 time steps.\n",
      "episode: 122, finish 199 time steps.\n",
      "episode: 123, finish 164 time steps.\n",
      "episode: 124, finish 80 time steps.\n",
      "episode: 125, finish 42 time steps.\n",
      "episode: 126, finish 135 time steps.\n",
      "episode: 127, finish 46 time steps.\n",
      "episode: 128, finish 42 time steps.\n",
      "episode: 129, finish 199 time steps.\n",
      "episode: 130, finish 112 time steps.\n",
      "episode: 131, finish 18 time steps.\n",
      "episode: 132, finish 17 time steps.\n",
      "episode: 133, finish 8 time steps.\n",
      "episode: 134, finish 55 time steps.\n",
      "episode: 135, finish 113 time steps.\n",
      "episode: 136, finish 39 time steps.\n",
      "episode: 137, finish 198 time steps.\n",
      "episode: 138, finish 130 time steps.\n",
      "episode: 139, finish 199 time steps.\n",
      "episode: 140, finish 37 time steps.\n",
      "episode: 141, finish 48 time steps.\n",
      "episode: 142, finish 42 time steps.\n",
      "episode: 143, finish 170 time steps.\n",
      "episode: 144, finish 176 time steps.\n",
      "episode: 145, finish 199 time steps.\n",
      "episode: 146, finish 136 time steps.\n",
      "episode: 147, finish 94 time steps.\n",
      "episode: 148, finish 199 time steps.\n",
      "episode: 149, finish 190 time steps.\n",
      "episode: 150, finish 95 time steps.\n",
      "episode: 151, finish 199 time steps.\n",
      "episode: 152, finish 34 time steps.\n",
      "episode: 153, finish 24 time steps.\n",
      "episode: 154, finish 180 time steps.\n",
      "episode: 155, finish 103 time steps.\n",
      "episode: 156, finish 157 time steps.\n",
      "episode: 157, finish 199 time steps.\n",
      "episode: 158, finish 140 time steps.\n",
      "episode: 159, finish 154 time steps.\n",
      "episode: 160, finish 83 time steps.\n",
      "episode: 161, finish 148 time steps.\n",
      "episode: 162, finish 86 time steps.\n",
      "episode: 163, finish 87 time steps.\n",
      "episode: 164, finish 145 time steps.\n",
      "episode: 165, finish 139 time steps.\n",
      "episode: 166, finish 199 time steps.\n",
      "episode: 167, finish 84 time steps.\n",
      "episode: 168, finish 191 time steps.\n",
      "episode: 169, finish 162 time steps.\n",
      "episode: 170, finish 137 time steps.\n",
      "episode: 171, finish 115 time steps.\n",
      "episode: 172, finish 117 time steps.\n",
      "episode: 173, finish 199 time steps.\n",
      "episode: 174, finish 199 time steps.\n",
      "episode: 175, finish 199 time steps.\n",
      "episode: 176, finish 90 time steps.\n",
      "episode: 177, finish 199 time steps.\n",
      "episode: 178, finish 199 time steps.\n",
      "episode: 179, finish 199 time steps.\n",
      "episode: 180, finish 125 time steps.\n",
      "episode: 181, finish 199 time steps.\n",
      "episode: 182, finish 199 time steps.\n",
      "episode: 183, finish 199 time steps.\n",
      "episode: 184, finish 199 time steps.\n",
      "episode: 185, finish 199 time steps.\n",
      "episode: 186, finish 199 time steps.\n",
      "episode: 187, finish 199 time steps.\n",
      "episode: 188, finish 199 time steps.\n",
      "episode: 189, finish 199 time steps.\n",
      "episode: 190, finish 199 time steps.\n",
      "continue success(step > 195) more than 10 times \n",
      "episode: 191, finish 199 time steps.\n"
     ]
    }
   ],
   "source": [
    "env = gym.make('CartPole-v0')\n",
    "env.reset()\n",
    "action_space = env.action_space\n",
    "n_states = env.observation_space.shape[0]\n",
    "\n",
    "agent = Agent(action_space, n_states)\n",
    "\n",
    "max_episodes = 1000\n",
    "max_steps = 200\n",
    "\n",
    "continue_success_episodes = 0\n",
    "learning_finish_flag = False\n",
    "\n",
    "frames = []\n",
    "\n",
    "for episode in range(max_episodes):\n",
    "    obs = env.reset()\n",
    "    for step in range(max_steps):\n",
    "        if learning_finish_flag:\n",
    "            frames.append(env.render(mode='rgb_array'))\n",
    "        action = agent.choose_action(obs, episode)\n",
    "        obs_next, _, done, _ = env.step(action)\n",
    "        if done:\n",
    "            if step < 195:\n",
    "                reward = -1\n",
    "                continue_success_episodes = 0\n",
    "            else:\n",
    "                reward = 1\n",
    "                continue_success_episodes += 1\n",
    "        else:\n",
    "            reward = 0\n",
    "        \n",
    "        agent.q_learning(obs, action, reward, obs_next)\n",
    "        \n",
    "        if done:\n",
    "            print(f'episode: {episode}, finish {step} time steps.')\n",
    "            break\n",
    "            \n",
    "        obs = obs_next\n",
    "        \n",
    "    if learning_finish_flag:\n",
    "        break\n",
    "    if continue_success_episodes >= 10:\n",
    "        learning_finish_flag = True\n",
    "        print(f'continue success(step > 195) more than 10 times ')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-03-07T14:27:17.476903Z",
     "start_time": "2023-03-07T14:25:53.586819Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<link rel=\"stylesheet\"\n",
       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/css/font-awesome.min.css\">\n",
       "<script language=\"javascript\">\n",
       "  function isInternetExplorer() {\n",
       "    ua = navigator.userAgent;\n",
       "    /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
       "    return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
       "  }\n",
       "\n",
       "  /* Define the Animation class */\n",
       "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
       "    this.img_id = img_id;\n",
       "    this.slider_id = slider_id;\n",
       "    this.loop_select_id = loop_select_id;\n",
       "    this.interval = interval;\n",
       "    this.current_frame = 0;\n",
       "    this.direction = 0;\n",
       "    this.timer = null;\n",
       "    this.frames = new Array(frames.length);\n",
       "\n",
       "    for (var i=0; i<frames.length; i++)\n",
       "    {\n",
       "     this.frames[i] = new Image();\n",
       "     this.frames[i].src = frames[i];\n",
       "    }\n",
       "    var slider = document.getElementById(this.slider_id);\n",
       "    slider.max = this.frames.length - 1;\n",
       "    if (isInternetExplorer()) {\n",
       "        // switch from oninput to onchange because IE <= 11 does not conform\n",
       "        // with W3C specification. It ignores oninput and onchange behaves\n",
       "        // like oninput. In contrast, Microsoft Edge behaves correctly.\n",
       "        slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
       "        slider.setAttribute('oninput', null);\n",
       "    }\n",
       "    this.set_frame(this.current_frame);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.get_loop_state = function(){\n",
       "    var button_group = document[this.loop_select_id].state;\n",
       "    for (var i = 0; i < button_group.length; i++) {\n",
       "        var button = button_group[i];\n",
       "        if (button.checked) {\n",
       "            return button.value;\n",
       "        }\n",
       "    }\n",
       "    return undefined;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.set_frame = function(frame){\n",
       "    this.current_frame = frame;\n",
       "    document.getElementById(this.img_id).src =\n",
       "            this.frames[this.current_frame].src;\n",
       "    document.getElementById(this.slider_id).value = this.current_frame;\n",
       "  }\n",
       "\n",
       "  Animation.prototype.next_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.previous_frame = function()\n",
       "  {\n",
       "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
       "  }\n",
       "\n",
       "  Animation.prototype.first_frame = function()\n",
       "  {\n",
       "    this.set_frame(0);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.last_frame = function()\n",
       "  {\n",
       "    this.set_frame(this.frames.length - 1);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.slower = function()\n",
       "  {\n",
       "    this.interval /= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.faster = function()\n",
       "  {\n",
       "    this.interval *= 0.7;\n",
       "    if(this.direction > 0){this.play_animation();}\n",
       "    else if(this.direction < 0){this.reverse_animation();}\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_forward = function()\n",
       "  {\n",
       "    this.current_frame += 1;\n",
       "    if(this.current_frame < this.frames.length){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.first_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.last_frame();\n",
       "        this.reverse_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.last_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.anim_step_reverse = function()\n",
       "  {\n",
       "    this.current_frame -= 1;\n",
       "    if(this.current_frame >= 0){\n",
       "      this.set_frame(this.current_frame);\n",
       "    }else{\n",
       "      var loop_state = this.get_loop_state();\n",
       "      if(loop_state == \"loop\"){\n",
       "        this.last_frame();\n",
       "      }else if(loop_state == \"reflect\"){\n",
       "        this.first_frame();\n",
       "        this.play_animation();\n",
       "      }else{\n",
       "        this.pause_animation();\n",
       "        this.first_frame();\n",
       "      }\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.pause_animation = function()\n",
       "  {\n",
       "    this.direction = 0;\n",
       "    if (this.timer){\n",
       "      clearInterval(this.timer);\n",
       "      this.timer = null;\n",
       "    }\n",
       "  }\n",
       "\n",
       "  Animation.prototype.play_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = 1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_forward();\n",
       "    }, this.interval);\n",
       "  }\n",
       "\n",
       "  Animation.prototype.reverse_animation = function()\n",
       "  {\n",
       "    this.pause_animation();\n",
       "    this.direction = -1;\n",
       "    var t = this;\n",
       "    if (!this.timer) this.timer = setInterval(function() {\n",
       "        t.anim_step_reverse();\n",
       "    }, this.interval);\n",
       "  }\n",
       "</script>\n",
       "\n",
       "<style>\n",
       ".animation {\n",
       "    display: inline-block;\n",
       "    text-align: center;\n",
       "}\n",
       "input[type=range].anim-slider {\n",
       "    width: 374px;\n",
       "    margin-left: auto;\n",
       "    margin-right: auto;\n",
       "}\n",
       ".anim-buttons {\n",
       "    margin: 8px 0px;\n",
       "}\n",
       ".anim-buttons button {\n",
       "    padding: 0;\n",
       "    width: 36px;\n",
       "}\n",
       ".anim-state label {\n",
       "    margin-right: 8px;\n",
       "}\n",
       ".anim-state input {\n",
       "    margin: 0;\n",
       "    vertical-align: middle;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<div class=\"animation\">\n",
       "  <img id=\"_anim_img4673a352bdbd44128a38cab439c2ff52\">\n",
       "  <div class=\"anim-controls\">\n",
       "    <input id=\"_anim_slider4673a352bdbd44128a38cab439c2ff52\" type=\"range\" class=\"anim-slider\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           oninput=\"anim4673a352bdbd44128a38cab439c2ff52.set_frame(parseInt(this.value));\"></input>\n",
       "    <div class=\"anim-buttons\">\n",
       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"anim4673a352bdbd44128a38cab439c2ff52.slower()\">\n",
       "          <i class=\"fa fa-minus\"></i></button>\n",
       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"anim4673a352bdbd44128a38cab439c2ff52.first_frame()\">\n",
       "        <i class=\"fa fa-fast-backward\"></i></button>\n",
       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"anim4673a352bdbd44128a38cab439c2ff52.previous_frame()\">\n",
       "          <i class=\"fa fa-step-backward\"></i></button>\n",
       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"anim4673a352bdbd44128a38cab439c2ff52.reverse_animation()\">\n",
       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"anim4673a352bdbd44128a38cab439c2ff52.pause_animation()\">\n",
       "          <i class=\"fa fa-pause\"></i></button>\n",
       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"anim4673a352bdbd44128a38cab439c2ff52.play_animation()\">\n",
       "          <i class=\"fa fa-play\"></i></button>\n",
       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"anim4673a352bdbd44128a38cab439c2ff52.next_frame()\">\n",
       "          <i class=\"fa fa-step-forward\"></i></button>\n",
       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"anim4673a352bdbd44128a38cab439c2ff52.last_frame()\">\n",
       "          <i class=\"fa fa-fast-forward\"></i></button>\n",
       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"anim4673a352bdbd44128a38cab439c2ff52.faster()\">\n",
       "          <i class=\"fa fa-plus\"></i></button>\n",
       "    </div>\n",
       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_select4673a352bdbd44128a38cab439c2ff52\"\n",
       "          class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_4673a352bdbd44128a38cab439c2ff52\"\n",
       "             >\n",
       "      <label for=\"_anim_radio1_4673a352bdbd44128a38cab439c2ff52\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_4673a352bdbd44128a38cab439c2ff52\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio2_4673a352bdbd44128a38cab439c2ff52\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_4673a352bdbd44128a38cab439c2ff52\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_4673a352bdbd44128a38cab439c2ff52\">Reflect</label>\n",
       "    </form>\n",
       "  </div>\n",
       "</div>\n",
       "\n",
       "\n",
       "<script language=\"javascript\">\n",
       "  /* Instantiate the Animation class. */\n",
       "  /* The IDs given should match those used in the template above. */\n",
       "  (function() {\n",
       "    var img_id = \"_anim_img4673a352bdbd44128a38cab439c2ff52\";\n",
       "    var slider_id = \"_anim_slider4673a352bdbd44128a38cab439c2ff52\";\n",
       "    var loop_select_id = \"_anim_loop_select4673a352bdbd44128a38cab439c2ff52\";\n",
       "    var frames = new Array(200);\n",
       "    \n",
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       "ofK4OAAAAABJRU5ErkJggg==\\\n",
       "\"\n",
       "\n",
       "\n",
       "    /* set a timeout to make sure all the above elements are created before\n",
       "       the object is initialized. */\n",
       "    setTimeout(function() {\n",
       "        anim4673a352bdbd44128a38cab439c2ff52 = new Animation(frames, img_id, slider_id, 50.0,\n",
       "                                 loop_select_id);\n",
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       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 1200x800 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "display_frames_as_gif(frames, output='./save/cart_pole_q_learrning.gif')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
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    "version": 3
   },
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   "title_cell": "Table of Contents",
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   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}