exp/3_windy_gridworld.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
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   "source": [
    "# Windy Gridworld\n",
    "\n",
    "`通过这个实验，了解Model Free的Temporal Difference的On-Policy Controlling，SARSA。`\n",
    "\n",
    "所有的实验源代码都在`lib`目录下，来自[dennybritz](https://github.com/dennybritz/reinforcement-learning)，这里只做解读和归总。\n",
    "\n",
    "## 实验目录\n",
    "\n",
    "- [Gridworld](https://applenob.github.io/gridworld.html)：对应MDP的Dynamic Programming\n",
    "- [Blackjack](https://applenob.github.io/black_jack.html)：对应Model Free的Monte Carlo的Planning和Controlling\n",
    "- [Windy Gridworld](https://applenob.github.io/windy_gridworld.html)：对应Model Free的Temporal Difference的On-Policy Controlling，SARSA。\n",
    "- [Cliff Walking](https://applenob.github.io/cliff_walking.html)：对应Model Free的Temporal Difference的Off-Policy Controlling，Q-learning。\n",
    "- [Mountain Car](https://applenob.github.io/mountain_car.html)：对应Q-Learning with Linear Function Approximation。\n",
    "- [Atari](https://applenob.github.io/atari.html)：对应Deep-Q Learning。\n",
    "\n",
    "\n",
    "## 本文目录\n",
    "\n",
    "- [问题介绍](#问题介绍)\n",
    "- [SARSA](#SARSA)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 问题介绍\n",
    "\n",
    "![](https://github.com/applenob/rl_learn/raw/master/res/windy_gw.png)\n",
    "\n",
    "类似于Gridworld，agent需要找到Terminate点，对应图中也就是在$S$点到$G$点。但是这个问题加入一个新的挑战，即会有自下而上往上吹的风，上图中横坐标的个数就代表风力。\n",
    "\n",
    "- 动作集：上下左右。\n",
    "- 奖励：每走一步减一分，到达终点加一分。\n",
    "- 这个问题实际上也可以用环境的模型来解决：在某个状态采取某个动作，计算进风力，你可以知道下一时刻会到哪里。但这里选择用用Model Free的方法解决。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "```python\n",
    "import gym\n",
    "import numpy as np\n",
    "import sys\n",
    "from gym.envs.toy_text import discrete\n",
    "\n",
    "UP = 0\n",
    "RIGHT = 1\n",
    "DOWN = 2\n",
    "LEFT = 3\n",
    "\n",
    "class WindyGridworldEnv(discrete.DiscreteEnv):\n",
    "\n",
    "    metadata = {'render.modes': ['human', 'ansi']}\n",
    "\n",
    "    def _limit_coordinates(self, coord):\n",
    "        \"\"\"返回合法的坐标\"\"\"\n",
    "        coord[0] = min(coord[0], self.shape[0] - 1)\n",
    "        coord[0] = max(coord[0], 0)\n",
    "        coord[1] = min(coord[1], self.shape[1] - 1)\n",
    "        coord[1] = max(coord[1], 0)\n",
    "        return coord\n",
    "\n",
    "    def _calculate_transition_prob(self, current, delta, winds):\n",
    "        \"\"\"采用某个action以后，下一个时刻的状态\"\"\"\n",
    "        new_position = np.array(current) + np.array(delta) + np.array([-1, 0]) * winds[tuple(current)]\n",
    "        new_position = self._limit_coordinates(new_position).astype(int)\n",
    "        new_state = np.ravel_multi_index(tuple(new_position), self.shape)\n",
    "        is_done = tuple(new_position) == (3, 7)  # 终点坐标\n",
    "        return [(1.0, new_state, -1.0, is_done)]\n",
    "\n",
    "    def __init__(self):\n",
    "        self.shape = (7, 10)\n",
    "\n",
    "        nS = np.prod(self.shape)\n",
    "        nA = 4\n",
    "\n",
    "        # Wind strength\n",
    "        # 风力已知\n",
    "        winds = np.zeros(self.shape)\n",
    "        winds[:,[3,4,5,8]] = 1\n",
    "        winds[:,[6,7]] = 2\n",
    "\n",
    "        # Calculate transition probabilities\n",
    "        P = {}\n",
    "        for s in range(nS):\n",
    "            # numpy.unravel_index：输入index（一维）和矩阵的shape，返回这个index对应在矩阵中的多维的index\n",
    "            position = np.unravel_index(s, self.shape)\n",
    "            P[s] = { a : [] for a in range(nA) }\n",
    "            P[s][UP] = self._calculate_transition_prob(position, [-1, 0], winds)\n",
    "            P[s][RIGHT] = self._calculate_transition_prob(position, [0, 1], winds)\n",
    "            P[s][DOWN] = self._calculate_transition_prob(position, [1, 0], winds)\n",
    "            P[s][LEFT] = self._calculate_transition_prob(position, [0, -1], winds)\n",
    "\n",
    "        # We always start in state (3, 0)\n",
    "        isd = np.zeros(nS)\n",
    "        # np.ravel_multi_index是numpy.unravel_index的逆操作\n",
    "        isd[np.ravel_multi_index((3,0), self.shape)] = 1.0\n",
    "\n",
    "        super(WindyGridworldEnv, self).__init__(nS, nA, P, isd)\n",
    "\n",
    "    def _render(self, mode='human', close=False):\n",
    "        if close:\n",
    "            return\n",
    "\n",
    "        outfile = StringIO() if mode == 'ansi' else sys.stdout\n",
    "\n",
    "        for s in range(self.nS):\n",
    "            position = np.unravel_index(s, self.shape)\n",
    "            # print(self.s)\n",
    "            if self.s == s:\n",
    "                output = \" x \"\n",
    "            elif position == (3,7):\n",
    "                output = \" T \"\n",
    "            else:\n",
    "                output = \" o \"\n",
    "\n",
    "            if position[1] == 0:\n",
    "                output = output.lstrip()\n",
    "            if position[1] == self.shape[1] - 1:\n",
    "                output = output.rstrip()\n",
    "                output += \"\\n\"\n",
    "\n",
    "            outfile.write(output)\n",
    "        outfile.write(\"\\n\")\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import gym\n",
    "import itertools\n",
    "import matplotlib\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import sys\n",
    "from collections import defaultdict\n",
    "from lib.envs.windy_gridworld import WindyGridworldEnv\n",
    "from lib import plotting\n",
    "\n",
    "matplotlib.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "试着往右走一步，会发生什么情况："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "30\n",
      "o  o  o  o  o  o  o  o  o  o\n",
      "o  o  o  o  o  o  o  o  o  o\n",
      "o  o  o  o  o  o  o  o  o  o\n",
      "x  o  o  o  o  o  o  T  o  o\n",
      "o  o  o  o  o  o  o  o  o  o\n",
      "o  o  o  o  o  o  o  o  o  o\n",
      "o  o  o  o  o  o  o  o  o  o\n",
      "\n",
      "(31, -1.0, False, {'prob': 1.0})\n",
      "o  o  o  o  o  o  o  o  o  o\n",
      "o  o  o  o  o  o  o  o  o  o\n",
      "o  o  o  o  o  o  o  o  o  o\n",
      "o  x  o  o  o  o  o  T  o  o\n",
      "o  o  o  o  o  o  o  o  o  o\n",
      "o  o  o  o  o  o  o  o  o  o\n",
      "o  o  o  o  o  o  o  o  o  o\n",
      "\n"
     ]
    }
   ],
   "source": [
    "env = WindyGridworldEnv()\n",
    "\n",
    "print(env.reset())\n",
    "env.render()\n",
    "\n",
    "print(env.step(1))\n",
    "env.render()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SARSA\n",
    "![](https://github.com/applenob/rl_learn/raw/master/res/sarsa_est.png)\n",
    "\n",
    "SARSA相当于差分版的On-Policy Monte-Carlo Control。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def make_epsilon_greedy_policy(Q, epsilon, nA):\n",
    "    \"\"\"\n",
    "    Creates an epsilon-greedy policy based on a given Q-function and epsilon.\n",
    "    \n",
    "    Args:\n",
    "        Q: A dictionary that maps from state -> action-values.\n",
    "            Each value is a numpy array of length nA (see below)\n",
    "        epsilon: The probability to select a random action . float between 0 and 1.\n",
    "        nA: Number of actions in the environment.\n",
    "    \n",
    "    Returns:\n",
    "        A function that takes the observation as an argument and returns\n",
    "        the probabilities for each action in the form of a numpy array of length nA.\n",
    "    \n",
    "    \"\"\"\n",
    "    def policy_fn(observation):\n",
    "        A = np.ones(nA, dtype=float) * epsilon / nA\n",
    "        best_action = np.argmax(Q[observation])\n",
    "        A[best_action] += (1.0 - epsilon)\n",
    "        return A\n",
    "    return policy_fn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sarsa(env, num_episodes, discount_factor=1.0, alpha=0.5, epsilon=0.1):\n",
    "    \"\"\"\n",
    "    SARSA algorithm: On-policy TD control. Finds the optimal epsilon-greedy policy.\n",
    "    \n",
    "    Args:\n",
    "        env: OpenAI environment.\n",
    "        num_episodes: Number of episodes to run for.\n",
    "        discount_factor: Lambda time discount factor.\n",
    "        alpha: TD learning rate.\n",
    "        epsilon: Chance the sample a random action. Float betwen 0 and 1.\n",
    "    \n",
    "    Returns:\n",
    "        A tuple (Q, stats).\n",
    "        Q is the optimal action-value function, a dictionary mapping state -> action values.\n",
    "        stats is an EpisodeStats object with two numpy arrays for episode_lengths and episode_rewards.\n",
    "    \"\"\"\n",
    "    \n",
    "    # The final action-value function.\n",
    "    # A nested dictionary that maps state -> (action -> action-value).\n",
    "    Q = defaultdict(lambda: np.zeros(env.action_space.n))\n",
    "    \n",
    "    # Keeps track of useful statistics\n",
    "    stats = plotting.EpisodeStats(\n",
    "        episode_lengths=np.zeros(num_episodes),\n",
    "        episode_rewards=np.zeros(num_episodes))\n",
    "\n",
    "    # The policy we're following\n",
    "    policy = make_epsilon_greedy_policy(Q, epsilon, env.action_space.n)\n",
    "    \n",
    "    for i_episode in range(num_episodes):\n",
    "        # Print out which episode we're on, useful for debugging.\n",
    "        if (i_episode + 1) % 100 == 0:\n",
    "            print(\"\\rEpisode {}/{}.\".format(i_episode + 1, num_episodes), end=\"\")\n",
    "            sys.stdout.flush()\n",
    "        \n",
    "        # Reset the environment and pick the first action\n",
    "        state = env.reset()\n",
    "        action_probs = policy(state)\n",
    "        action = np.random.choice(np.arange(len(action_probs)), p=action_probs)\n",
    "        \n",
    "        # MC是抽完一整条episode，再用这条episode进行更新。\n",
    "        # SARSA在抽episode的每一步都要进行更新。\n",
    "        \n",
    "        # One step in the environment\n",
    "        # itertools.count()：从0开始计数\n",
    "        for t in itertools.count():\n",
    "            # Take a step\n",
    "            next_state, reward, done, _ = env.step(action)\n",
    "            \n",
    "            # Pick the next action\n",
    "            next_action_probs = policy(next_state)\n",
    "            next_action = np.random.choice(np.arange(len(next_action_probs)), p=next_action_probs)\n",
    "            \n",
    "            # Update statistics\n",
    "            stats.episode_rewards[i_episode] += reward\n",
    "            stats.episode_lengths[i_episode] = t\n",
    "            \n",
    "            # TD Update\n",
    "            td_target = reward + discount_factor * Q[next_state][next_action]\n",
    "            td_delta = td_target - Q[state][action]\n",
    "            Q[state][action] += alpha * td_delta\n",
    "    \n",
    "            if done:\n",
    "                break\n",
    "                \n",
    "            action = next_action\n",
    "            state = next_state        \n",
    "    \n",
    "    return Q, stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "价值函数更新：$Q(S,A)\\leftarrow Q(S,A)+\\alpha[R+\\gamma Q(S',A')-Q(S, A)]$\n",
    "\n",
    "对应代码：\n",
    "```python\n",
    "td_target = reward + discount_factor * Q[next_state][next_action]\n",
    "td_delta = td_target - Q[state][action]\n",
    "Q[state][action] += alpha * td_delta\n",
    "```\n",
    "可以说是一一对应。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Episode 200/200."
     ]
    }
   ],
   "source": [
    "Q, stats = sarsa(env, 200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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uzumY2WxGTQ2X09Dp3amyectBREREbYJLIa59+/bYvn2707GdO3eiY8eOHilU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\nU62C7sUfAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcf06b0e048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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HhIQo5axSqTB27FisWrVKWb9q1SqMGTMGKpX8MRAeHo6vvvpKrxxKn7vy5ezn51fjgTM1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\nACCAEeYAAAAC2P8HCLxv7qX7MEIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcf06a44f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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/UfOI+9Lt3r0bn88HwM6dO8nIyKBBgwZexRQRETmK3bMb3/R74cfNOCP/hNP1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\n3wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcf06ab7a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(<matplotlib.figure.Figure at 0x7fcf06b0e048>,\n",
       " <matplotlib.figure.Figure at 0x7fcf06a44f60>,\n",
       " <matplotlib.figure.Figure at 0x7fcf06ab7a58>)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plotting.plot_episode_stats(stats)"
   ]
  }
 ],
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