{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-20T15:09:34.179156Z",
     "start_time": "2023-02-20T15:09:33.559589Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import gym\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-20T15:09:36.809994Z",
     "start_time": "2023-02-20T15:09:36.373146Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5, 5))\n",
    "ax = plt.gca()\n",
    "ax.set_xlim(0, 3)\n",
    "ax.set_ylim(0, 3)\n",
    "\n",
    "# plt.plot([1, 1], [0, 1], color='red', linewidth=2)\n",
    "# plt.plot([1, 2], [2, 2], color='red', linewidth=2)\n",
    "# plt.plot([2, 2], [2, 1], color='red', linewidth=2)\n",
    "# plt.plot([2, 3], [1, 1], color='red', linewidth=2)\n",
    "\n",
    "plt.plot([2, 3], [1, 1], color='red', linewidth=2)\n",
    "plt.plot([0, 1], [1, 1], color='red', linewidth=2)\n",
    "plt.plot([1, 1], [1, 2], color='red', linewidth=2)\n",
    "plt.plot([1, 2], [2, 2], color='red', linewidth=2)\n",
    "\n",
    "plt.text(0.5, 2.5, 'S0', size=14, ha='center')\n",
    "plt.text(1.5, 2.5, 'S1', size=14, ha='center')\n",
    "plt.text(2.5, 2.5, 'S2', size=14, ha='center')\n",
    "plt.text(0.5, 1.5, 'S3', size=14, ha='center')\n",
    "plt.text(1.5, 1.5, 'S4', size=14, ha='center')\n",
    "plt.text(2.5, 1.5, 'S5', size=14, ha='center')\n",
    "plt.text(0.5, 0.5, 'S6', size=14, ha='center')\n",
    "plt.text(1.5, 0.5, 'S7', size=14, ha='center')\n",
    "plt.text(2.5, 0.5, 'S8', size=14, ha='center')\n",
    "plt.text(0.5, 2.3, 'START', ha='center')\n",
    "plt.text(2.5, 0.3, 'GOAL', ha='center')\n",
    "# plt.axis('off')\n",
    "plt.tick_params(axis='both', which='both', \n",
    "                bottom=False, top=False, \n",
    "                right=False, left=False,\n",
    "                labelbottom=False, labelleft=False\n",
    "               )\n",
    "line, = ax.plot([0.5], [2.5], marker='o', color='g', markersize=60)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-19T01:21:55.938956Z",
     "start_time": "2023-02-19T01:21:55.936601Z"
    }
   },
   "source": [
    "## basics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 基本概念及术语\n",
    "    - algorithm\n",
    "        - policy iteration\n",
    "            - policy gradient\n",
    "        - value iteration\n",
    "            - sarsa： state, action, reward, state, action\n",
    "                - Q-table：待学习（learning/iteration update)\n",
    "                    - row index: state; column index: action;\n",
    "                    - 不是概率分布，是 value\n",
    "            - q-learning\n",
    "    - reward\n",
    "        - 特定时间 $t$ 给到的奖励 $R_t$ 称为即时奖励（immediate reward）\n",
    "        - 未来的总奖励 $G_t$\n",
    "            - $G_t=R_{t+1}+R_{t+2}+R_{t+3}+\\cdots$\n",
    "            - $G_t=R_{t+1}+\\gamma R_{t+2}+\\gamma^2R_{t+3} + \\cdots + \\gamma^kR_{t+k+1}\\cdots$\n",
    "        - 举例\n",
    "            - $Q_\\pi(s=7,a=1)=R_{t+1}=1$\n",
    "            - $Q_\\pi(s=7,a=0)=\\gamma^2$\n",
    "    - action value，state value\n",
    "    - bellman equation\n",
    "        - 适用于状态价值函数（state value function），也适用于动作价值函数（action value function）\n",
    "    - mdp：markov decision process\n",
    "        - 马尔可夫性\n",
    "            - $p(s_{t+1}|s_t)=p(s_{t+1}|{s_1,s_2,s_3,\\cdots,s_t})$\n",
    "        - bellman equation 成立的前提条件"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-19T01:22:33.918570Z",
     "start_time": "2023-02-19T01:22:33.812489Z"
    }
   },
   "source": [
    "- $R_t$\n",
    "- $Q_{\\pi}(s,a)$：state action value function\n",
    "    - Q table\n",
    "    - 通过 Sarsa 算法迭代更新 $Q_{\\pi}(s,a)$\n",
    "- 对于强化学习而言\n",
    "    - state, action, reward 都是需要精心设计的"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sarsa（state action reward state action）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-20T15:20:32.328550Z",
     "start_time": "2023-02-20T15:20:32.322841Z"
    }
   },
   "outputs": [],
   "source": [
    "# border & barrier\n",
    "# ↑, →, ↓, ←（顺时针）\n",
    "# row index: given state\n",
    "# col index: posible action\n",
    "# (state, action) matrix\n",
    "# 跟环境对齐\n",
    "theta_0 = np.asarray([[np.nan, 1, 1, np.nan],      # s0\n",
    "                      [np.nan, 1, np.nan, 1],      # s1\n",
    "                      [np.nan, np.nan, 1, 1],      # s2\n",
    "                      [1, np.nan, np.nan, np.nan], # s3 \n",
    "                      [np.nan, 1, 1, np.nan],      # s4\n",
    "                      [1, np.nan, np.nan, 1],      # s5\n",
    "                      [np.nan, 1, np.nan, np.nan], # s6 \n",
    "                      [1, 1, np.nan, 1]]           # s7\n",
    "                     )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-20T15:20:33.445898Z",
     "start_time": "2023-02-20T15:20:33.443279Z"
    }
   },
   "outputs": [],
   "source": [
    "n_states, n_actions = theta_0.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-20T15:22:28.342788Z",
     "start_time": "2023-02-20T15:22:28.340225Z"
    }
   },
   "outputs": [],
   "source": [
    "# Q table, 状态是离散的（s0-s7），动作也是离散的（上右下左）\n",
    "Q = np.random.rand(n_states, n_actions) * theta_0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-20T15:22:29.712906Z",
     "start_time": "2023-02-20T15:22:29.702001Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[       nan, 0.05711349, 0.7487308 ,        nan],\n",
       "       [       nan, 0.21055329,        nan, 0.34236513],\n",
       "       [       nan,        nan, 0.58900823, 0.12580755],\n",
       "       [0.19742577,        nan,        nan,        nan],\n",
       "       [       nan, 0.46973656, 0.03069312,        nan],\n",
       "       [0.90690458,        nan,        nan, 0.67280829],\n",
       "       [       nan, 0.18346137,        nan,        nan],\n",
       "       [0.40679226, 0.88075109,        nan, 0.38732487]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### $\\epsilon$-greedy (explore, exploit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-20T15:23:51.690714Z",
     "start_time": "2023-02-20T15:23:51.684199Z"
    }
   },
   "outputs": [],
   "source": [
    "# 基于占比, 最 naive 的概率化方式\n",
    "def cvt_theta_0_to_pi(theta):\n",
    "    m, n = theta.shape\n",
    "    pi = np.zeros((m, n))\n",
    "    for r in range(m):\n",
    "        pi[r, :] = theta[r, :] / np.nansum(theta[r, :])\n",
    "    return np.nan_to_num(pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-20T15:23:53.973666Z",
     "start_time": "2023-02-20T15:23:53.970002Z"
    }
   },
   "outputs": [],
   "source": [
    "pi_0 = cvt_theta_0_to_pi(theta_0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-20T15:23:59.386828Z",
     "start_time": "2023-02-20T15:23:59.382946Z"
    },
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.        , 0.5       , 0.5       , 0.        ],\n",
       "       [0.        , 0.5       , 0.        , 0.5       ],\n",
       "       [0.        , 0.        , 0.5       , 0.5       ],\n",
       "       [1.        , 0.        , 0.        , 0.        ],\n",
       "       [0.        , 0.5       , 0.5       , 0.        ],\n",
       "       [0.5       , 0.        , 0.        , 0.5       ],\n",
       "       [0.        , 1.        , 0.        , 0.        ],\n",
       "       [0.33333333, 0.33333333, 0.        , 0.33333333]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pi_0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-20T15:24:58.768881Z",
     "start_time": "2023-02-20T15:24:58.763948Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[       nan, 0.05711349, 0.7487308 ,        nan],\n",
       "       [       nan, 0.21055329,        nan, 0.34236513],\n",
       "       [       nan,        nan, 0.58900823, 0.12580755],\n",
       "       [0.19742577,        nan,        nan,        nan],\n",
       "       [       nan, 0.46973656, 0.03069312,        nan],\n",
       "       [0.90690458,        nan,        nan, 0.67280829],\n",
       "       [       nan, 0.18346137,        nan,        nan],\n",
       "       [0.40679226, 0.88075109,        nan, 0.38732487]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-19T01:33:27.896249Z",
     "start_time": "2023-02-19T01:33:27.893096Z"
    }
   },
   "outputs": [],
   "source": [
    "# epsilon-greedy\n",
    "def get_action(s, Q, eps, pi_0):\n",
    "    action_space = list(range(4))\n",
    "    # eps, explore\n",
    "    if np.random.rand() < eps:\n",
    "        action = np.random.choice(action_space, p=pi_0[s, :])\n",
    "    else:\n",
    "        # 1-eps, exploit\n",
    "        action = np.nanargmax(Q[s, :])\n",
    "    return action"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sarsa (update $Q_\\pi(s,a)$)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "理想情况下：\n",
    "$$\n",
    "Q(s_t,a_t) = R_{t+1}+\\gamma Q(s_{t+1}, a_{t+1})\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- td (temporal difference error)\n",
    "    - $R_{t+1}+\\gamma Q(s_{t+1},a_{t+1})-Q(s_t,a_t)$\n",
    "- final update equation\n",
    "    - $Q(s_t,a_t)=Q(s_t,a_t)+\\eta\\cdot(R_{t+1}+\\gamma Q(s_{t+1},a_{t+1})-Q(s_t,a_t))$\n",
    "    - $s_t,a_t,r_{t+1},s_{t+1},a_{t+1}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 折扣（discount factor，$\\gamma$）\n",
    "    - 有助于缩短步数（更快地结束任务）；"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-19T02:15:30.250510Z",
     "start_time": "2023-02-19T02:15:30.247289Z"
    }
   },
   "outputs": [],
   "source": [
    "def sarsa(s, a, r, s_next, a_next, Q, eta, gamma):\n",
    "    if s_next == 8:\n",
    "        Q[s, a] = Q[s, a] + eta * (r - Q[s, a])\n",
    "    else:\n",
    "        Q[s, a] = Q[s, a] + eta * (r + gamma * Q[s_next, a_next] - Q[s, a])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 解决 maze 问题"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-20T15:28:38.124516Z",
     "start_time": "2023-02-20T15:28:38.116963Z"
    }
   },
   "outputs": [],
   "source": [
    "# 维护着状态，以及 step 函数的返回\n",
    "class MazeEnv(gym.Env):\n",
    "    def __init__(self):\n",
    "        self.state = 0\n",
    "        pass\n",
    "    \n",
    "    def reset(self):\n",
    "        self.state = 0\n",
    "        return self.state\n",
    "    \n",
    "    def step(self, action):\n",
    "        if action == 0:\n",
    "            self.state -= 3\n",
    "        elif action == 1:\n",
    "            self.state += 1\n",
    "        elif action == 2:\n",
    "            self.state += 3\n",
    "        elif action == 3:\n",
    "            self.state -= 1\n",
    "        done = False\n",
    "        reward = 0\n",
    "        if self.state == 8:\n",
    "            done = True\n",
    "            reward = 1\n",
    "        # state, reward, done, _\n",
    "        return self.state, reward, done, {}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-20T15:33:26.797516Z",
     "start_time": "2023-02-20T15:33:26.783342Z"
    }
   },
   "outputs": [],
   "source": [
    "# 动作策略选择，基于当前环境的状态\n",
    "class Agent:\n",
    "    def __init__(self):\n",
    "        self.action_space = list(range(4))\n",
    "        self.theta_0 = np.asarray([[np.nan, 1, 1, np.nan],      # s0\n",
    "                      [np.nan, 1, np.nan, 1],      # s1\n",
    "                      [np.nan, np.nan, 1, 1],      # s2\n",
    "                      [1, np.nan, np.nan, np.nan], # s3 \n",
    "                      [np.nan, 1, 1, np.nan],      # s4\n",
    "                      [1, np.nan, np.nan, 1],      # s5\n",
    "                      [np.nan, 1, np.nan, np.nan], # s6 \n",
    "                      [1, 1, np.nan, 1]]           # s7\n",
    "                     )\n",
    "        self.pi = self._cvt_theta_to_pi()\n",
    "#         self.pi = self._softmax_cvt_theta_to_pi()\n",
    "#         self.theta = self.theta_0\n",
    "\n",
    "        self.Q = np.random.rand(*self.theta_0.shape) * self.theta_0\n",
    "        self.eta = 0.1\n",
    "        self.gamma = 0.9\n",
    "        self.eps = 0.5\n",
    "        \n",
    "    def _cvt_theta_to_pi(self):\n",
    "        m, n = self.theta_0.shape\n",
    "        pi = np.zeros((m, n))\n",
    "        for r in range(m):\n",
    "            pi[r, :] = self.theta_0[r, :] / np.nansum(self.theta_0[r, :])\n",
    "        return np.nan_to_num(pi)\n",
    "    \n",
    "#     def _softmax_cvt_theta_to_pi(self, beta=1.):\n",
    "#         m, n = self.theta.shape\n",
    "#         pi = np.zeros((m, n))\n",
    "#         exp_theta = np.exp(self.theta*beta)\n",
    "#         for r in range(m):\n",
    "#             pi[r, :] = exp_theta[r, :] / np.nansum(exp_theta[r, :])\n",
    "#         return np.nan_to_num(pi)\n",
    "    \n",
    "    def get_action(self, s):\n",
    "        # eps, explore\n",
    "        if np.random.rand() < self.eps:\n",
    "            action = np.random.choice(self.action_space, p=self.pi[s, :])\n",
    "        else:\n",
    "            # 1-eps, exploit\n",
    "            action = np.nanargmax(self.Q[s, :])\n",
    "        return action\n",
    "        \n",
    "    def sarsa(self, s, a, r, s_next, a_next):\n",
    "        if s_next == 8:\n",
    "            self.Q[s, a] = self.Q[s, a] + self.eta * (r - self.Q[s, a])\n",
    "        else:\n",
    "            self.Q[s, a] = self.Q[s, a] + self.eta * (r + self.gamma * self.Q[s_next, a_next] - self.Q[s, a])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 完成训练及更新"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-20T15:38:08.370694Z",
     "start_time": "2023-02-20T15:38:08.296970Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 0.48151692420235004 25\n",
      "2 0.788238427054541 51\n",
      "3 0.5193178707316495 73\n",
      "4 0.09357958369502378 23\n",
      "5 0.07459493697310315 7\n",
      "6 0.06891781188632101 7\n",
      "7 0.06585711141363843 7\n",
      "8 0.06265613413272358 7\n",
      "9 0.060100868881304614 7\n",
      "10 0.059287337144400654 7\n",
      "11 0.058488284106318955 7\n",
      "12 0.05750697273897609 7\n",
      "13 0.05634890213948618 7\n",
      "14 0.055022881405307755 7\n",
      "15 0.0535403609535367 7\n",
      "16 0.051914820609968326 7\n",
      "17 0.0501612179940748 7\n",
      "18 0.048295498355812816 7\n",
      "19 0.04633416520669903 7\n",
      "20 0.04509458086047741 7\n",
      "21 0.0443781660421414 7\n",
      "22 0.043566741048947755 7\n",
      "23 0.04266900608905749 7\n",
      "24 0.04169365931899821 7\n",
      "25 0.04064935278238613 7\n",
      "26 0.039544641494567434 7\n",
      "27 0.03877432598312053 7\n",
      "28 0.03836919489516444 7\n",
      "29 0.037932322993017575 7\n",
      "30 0.03746384259607333 7\n",
      "31 0.036964222794984625 7\n",
      "32 0.03643423557551101 7\n",
      "33 0.03587492225074168 7\n",
      "34 0.03528756047376702 7\n",
      "35 0.034673632089539 7\n",
      "36 0.034034792062826946 7\n",
      "37 0.03337283869172736 7\n",
      "38 0.032689685285438086 7\n",
      "39 0.031987333452767774 7\n",
      "40 0.03126784811552158 7\n",
      "41 0.030533334329512607 7\n",
      "42 0.02978591596630603 7\n",
      "43 0.02902771628138473 7\n",
      "44 0.02826084036961629 7\n",
      "45 0.0274873594868823 7\n",
      "46 0.026709297197557824 7\n",
      "47 0.02592861729120166 7\n",
      "48 0.025147213398248935 7\n",
      "49 0.024366900223515675 7\n",
      "50 0.023589406307802152 7\n",
      "51 0.022816368221570238 7\n",
      "52 0.022049326090399224 7\n",
      "53 0.021289720349440266 7\n",
      "54 0.020538889623210932 7\n",
      "55 0.019798069627555426 7\n",
      "56 0.01906839299226787 7\n",
      "57 0.018350889905525525 7\n",
      "58 0.01764648948474906 7\n",
      "59 0.01695602178262262 7\n",
      "60 0.016280220341618468 7\n",
      "61 0.01561972521537619 7\n",
      "62 0.014975086380526359 7\n",
      "63 0.01434676746795055 7\n",
      "64 0.013735149747947817 7\n",
      "65 0.013140536309220685 7\n",
      "66 0.012563156376991624 7\n",
      "67 0.012003169720803564 7\n",
      "68 0.011460671107647646 7\n",
      "69 0.01093569476093581 7\n",
      "70 0.010428218790478228 7\n",
      "71 0.009938169563017962 7\n",
      "72 0.009465425986993514 7\n",
      "73 0.009009823689056895 7\n",
      "74 0.00857115906343553 7\n",
      "75 0.00814919317852647 7\n",
      "76 0.007743655528121618 7\n",
      "77 0.0073542476174153215 7\n",
      "78 0.006980646376435584 7\n",
      "79 0.006622507395769972 7\n",
      "80 0.0062794679814730525 7\n",
      "81 0.005951150027797558 7\n",
      "82 0.00563716270797221 7\n",
      "83 0.005337104984597274 7\n",
      "84 0.005050567942414208 7\n",
      "85 0.004777136947210048 7\n",
      "86 0.004516393635464522 7\n",
      "87 0.004267917740051419 7\n",
      "88 0.004031288757878282 7\n",
      "89 0.0038060874658013555 7\n",
      "90 0.0035918972914945613 7\n",
      "91 0.0033883055462049505 7\n",
      "92 0.003194904526485076 7\n",
      "93 0.00301129249208143 7\n",
      "94 0.002837074527182959 7\n",
      "95 0.002671863292188603 7\n",
      "96 0.0025152796730716354 7\n",
      "97 0.002366953335290245 7\n",
      "98 0.002226523189017504 7\n",
      "99 0.002093637772283996 7\n",
      "100 0.001967955558394241 7\n",
      "101 0.0018491451937413528 7\n"
     ]
    }
   ],
   "source": [
    "maze = MazeEnv()\n",
    "agent = Agent()\n",
    "epoch = 0\n",
    "while True:\n",
    "    old_Q = np.nanmax(agent.Q, axis=1)\n",
    "    s = maze.reset()\n",
    "    a = agent.get_action(s)\n",
    "    s_a_history = [[s, np.nan]]\n",
    "    while True:\n",
    "        # s, a \n",
    "        s_a_history[-1][1] = a\n",
    "        s_next, reward, done, _ = maze.step(a, )\n",
    "        # s_next, a_next\n",
    "        s_a_history.append([s_next, np.nan])\n",
    "        if done:\n",
    "            a_next = np.nan\n",
    "        else:\n",
    "            a_next = agent.get_action(s_next)\n",
    "#         print(s, a, reward, s_next, a_next)\n",
    "        agent.sarsa(s, a, reward, s_next, a_next)\n",
    "#         print(agent.pi)\n",
    "        if done:\n",
    "            break\n",
    "        else:\n",
    "            a = a_next\n",
    "            s = maze.state\n",
    "\n",
    "    # s_s_history, agent.Q\n",
    "    update = np.sum(np.abs(np.nanmax(agent.Q, axis=1) - old_Q))\n",
    "    epoch +=1\n",
    "    agent.eps /= 2\n",
    "    print(epoch, update, len(s_a_history))\n",
    "    if epoch > 100 or update < 1e-5:\n",
    "        break\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-20T15:38:33.582285Z",
     "start_time": "2023-02-20T15:38:33.568692Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[       nan, 0.5741703 , 0.28654803,        nan],\n",
       "       [       nan, 0.64891149,        nan, 0.31090434],\n",
       "       [       nan,        nan, 0.72647909, 0.04574432],\n",
       "       [0.24347619,        nan,        nan,        nan],\n",
       "       [       nan, 0.34181286, 0.89988623,        nan],\n",
       "       [0.21120543,        nan,        nan, 0.80934131],\n",
       "       [       nan, 0.61078998,        nan,        nan],\n",
       "       [0.19954603, 0.99999028,        nan, 0.64883227]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "agent.Q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 可视化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-20T15:38:57.716413Z",
     "start_time": "2023-02-20T15:38:57.705590Z"
    }
   },
   "outputs": [],
   "source": [
    "from matplotlib import animation\n",
    "from IPython.display import HTML"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-20T15:38:58.576025Z",
     "start_time": "2023-02-20T15:38:58.572588Z"
    }
   },
   "outputs": [],
   "source": [
    "def init():\n",
    "    line.set_data([], [])\n",
    "    return (line, )\n",
    "def animate(i):\n",
    "    state = s_a_history[i][0]\n",
    "    x = (state % 3)+0.5\n",
    "    y = 2.5 - int(state/3)\n",
    "    line.set_data(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-20T15:39:00.248954Z",
     "start_time": "2023-02-20T15:39:00.244740Z"
    }
   },
   "outputs": [],
   "source": [
    "anim = animation.FuncAnimation(fig, animate, init_func=init, frames=len(s_a_history), interval=200, repeat=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2023-02-20T15:39:06.778021Z",
     "start_time": "2023-02-20T15:39:06.064615Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<link rel=\"stylesheet\"\n",
       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/\n",
       "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, Mircosoft 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_imgc5acd73a5e904014b0b55ceeef93725c\">\n",
       "  <div class=\"anim-controls\">\n",
       "    <input id=\"_anim_sliderc5acd73a5e904014b0b55ceeef93725c\" type=\"range\" class=\"anim-slider\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           oninput=\"animc5acd73a5e904014b0b55ceeef93725c.set_frame(parseInt(this.value));\"></input>\n",
       "    <div class=\"anim-buttons\">\n",
       "      <button onclick=\"animc5acd73a5e904014b0b55ceeef93725c.slower()\"><i class=\"fa fa-minus\"></i></button>\n",
       "      <button onclick=\"animc5acd73a5e904014b0b55ceeef93725c.first_frame()\"><i class=\"fa fa-fast-backward\">\n",
       "          </i></button>\n",
       "      <button onclick=\"animc5acd73a5e904014b0b55ceeef93725c.previous_frame()\">\n",
       "          <i class=\"fa fa-step-backward\"></i></button>\n",
       "      <button onclick=\"animc5acd73a5e904014b0b55ceeef93725c.reverse_animation()\">\n",
       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "      <button onclick=\"animc5acd73a5e904014b0b55ceeef93725c.pause_animation()\"><i class=\"fa fa-pause\">\n",
       "          </i></button>\n",
       "      <button onclick=\"animc5acd73a5e904014b0b55ceeef93725c.play_animation()\"><i class=\"fa fa-play\"></i>\n",
       "          </button>\n",
       "      <button onclick=\"animc5acd73a5e904014b0b55ceeef93725c.next_frame()\"><i class=\"fa fa-step-forward\">\n",
       "          </i></button>\n",
       "      <button onclick=\"animc5acd73a5e904014b0b55ceeef93725c.last_frame()\"><i class=\"fa fa-fast-forward\">\n",
       "          </i></button>\n",
       "      <button onclick=\"animc5acd73a5e904014b0b55ceeef93725c.faster()\"><i class=\"fa fa-plus\"></i></button>\n",
       "    </div>\n",
       "    <form action=\"#n\" name=\"_anim_loop_selectc5acd73a5e904014b0b55ceeef93725c\" class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_c5acd73a5e904014b0b55ceeef93725c\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio1_c5acd73a5e904014b0b55ceeef93725c\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_c5acd73a5e904014b0b55ceeef93725c\"\n",
       "             >\n",
       "      <label for=\"_anim_radio2_c5acd73a5e904014b0b55ceeef93725c\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_c5acd73a5e904014b0b55ceeef93725c\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_c5acd73a5e904014b0b55ceeef93725c\">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_imgc5acd73a5e904014b0b55ceeef93725c\";\n",
       "    var slider_id = \"_anim_sliderc5acd73a5e904014b0b55ceeef93725c\";\n",
       "    var loop_select_id = \"_anim_loop_selectc5acd73a5e904014b0b55ceeef93725c\";\n",
       "    var frames = new Array(7);\n",
       "    \n",
       "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAWgAAAFoCAYAAAB65WHVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\\\n",
       "AAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjEsIGh0\\\n",
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       "IQ1fKZrAJNCKELzEOtQqhk6iVYjl+oOqV+KgTin++tqxSGSw8rUyF2JRq/UnAq2WCBgLodJEKF6Q\\\n",
       "Kl+NQMAGUhBCfm7y+f6xhEtSQhJIcj67+3zMZFqyZzfvfCY+c3L27FmXMcYIAGCdMKcHAACcGYEG\\\n",
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       "\"\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",
       "        animc5acd73a5e904014b0b55ceeef93725c = new Animation(frames, img_id, slider_id, 200.0,\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"
    }
   ],
   "source": [
    "HTML(anim.to_jshtml())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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