Frozen lake VI with solution.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from __future__ import (absolute_import, division, print_function,\n",
    "                        unicode_literals)\n",
    "%matplotlib inline\n",
    "\n",
    "import time\n",
    "import seaborn\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import math\n",
    "import torch\n",
    "\n",
    "\n",
    "from gym.envs.toy_text.frozen_lake import LEFT, RIGHT, DOWN, UP\n",
    "from gym.envs.toy_text import frozen_lake, discrete\n",
    "\n",
    "import gym\n",
    "from gym.envs.registration import register\n",
    "\n",
    "register(\n",
    "    id='D4x4-FrozenLake-v0',\n",
    "    entry_point='gym.envs.toy_text.frozen_lake:FrozenLakeEnv',\n",
    "    kwargs={'map_name': '4x4',\n",
    "            'is_slippery': True})\n",
    "\n",
    "\n",
    "\"\"\" \n",
    "    env: gym.core.Environment\n",
    "    Environment to play on.\n",
    "\n",
    "    env.P: dictionary\n",
    "    It is from gym.core.Environment\n",
    "    P[state][action] is tuples with (probability, nextstate, reward, terminal)\n",
    "    \n",
    "    env.nS: int\n",
    "    count of states \n",
    "    \n",
    "    env.nA: int\n",
    "    count of actions available\n",
    "    \n",
    "    action_space: discrete\n",
    "                LEFT = 0\n",
    "                DOWN = 1\n",
    "                RIGHT = 2\n",
    "                UP = 3\n",
    "    ENVIRONMENT: \n",
    "                \"SFFF\",\n",
    "                \"FHFH\",\n",
    "                \"FFFH\",\n",
    "                \"HFFG\"\n",
    "\"\"\"\n",
    "\n",
    "def print_policy(policy, action_names):\n",
    "    \"\"\" \n",
    "    Print the policy in human-readable format.\n",
    "    \"\"\"\n",
    "    str_policy = policy.astype('str')\n",
    "    for action_num, action_name in action_names.items():\n",
    "        np.place(str_policy, policy == action_num, action_name)\n",
    "\n",
    "    print(str_policy[0:4])\n",
    "    print(str_policy[4:8])\n",
    "    print(str_policy[8:12])\n",
    "    print(str_policy[12:16])\n",
    "    \n",
    "    return str_policy\n",
    "\n",
    "action_names = {LEFT: 'LEFT', RIGHT: 'RIGHT', DOWN: 'DOWN', UP: 'UP'}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "env = gym.make('D4x4-FrozenLake-v0')\n",
    "grid = 4\n",
    "gamma = 0.9 # Change this to play with it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Doing Value Iteration\n",
      "Total time taken: 0.05970907211303711\n",
      "Value function: [0.07303611 0.06443395 0.07630225 0.05787118 0.09503288 0.\n",
      " 0.11304412 0.         0.14760918 0.24869516 0.30035868 0.\n",
      " 0.         0.38070441 0.63938156 0.        ]\n",
      "Total Value Iteration Steps: 27\n",
      "Policy:\n",
      "['LEFT' 'UP' 'LEFT' 'UP']\n",
      "['LEFT' 'LEFT' 'LEFT' 'LEFT']\n",
      "['UP' 'DOWN' 'LEFT' 'LEFT']\n",
      "['LEFT' 'RIGHT' 'DOWN' 'LEFT']\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Heatmap of policy iteration with value function values and directions')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 792x648 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "########################################################################\n",
    "######################### Value iteration ##############################\n",
    "########################################################################\n",
    "\n",
    "\n",
    "def value_iteration(env, gamma, max_iterations=int(1e3), tol=1e-3):\n",
    "    \"\"\"\n",
    "    Runs value iteration for a given gamma and environment. Return \n",
    "    the value function and the number of iterations it took to converge.\n",
    "        See section 4.4 of Reinforcement Learning: An Introduction (Adaptive Computation and Machine Learning) by Sutton and Barto\n",
    "    \"\"\"\n",
    "    value_func_old = np.random.rand(env.nS)\n",
    "    value_func_new = np.zeros(env.nS)\n",
    "    value_func_collect = np.zeros((env.nS,max_iterations))\n",
    "    delta_collect = np.zeros(max_iterations)\n",
    "\n",
    "    for iteration in range(max_iterations):\n",
    "        delta=0\n",
    "        for s in range(env.nS):\n",
    "            max_value_func = -1\n",
    "            \n",
    "            # Refer Figure 4.5 for the algorithm\n",
    "            # Parse through env.nA for finding the maximum\n",
    "            # Using env.P[s][a] implement the V(s) updation\n",
    "            for a in range(env.nA):\n",
    "                value_func_temp=0\n",
    "                for next_state_from_tpm in env.P[s][a]: \n",
    "                    prob_action = next_state_from_tpm[0]\n",
    "                    cur_reward=next_state_from_tpm[2]\n",
    "                    if next_state_from_tpm[3]:\n",
    "                        future_reward=0\n",
    "                    else: future_reward=gamma*value_func_old[next_state_from_tpm[1]]\n",
    "                    value_func_temp+=prob_action * (cur_reward + future_reward)\n",
    "                if value_func_temp>max_value_func:\n",
    "                    max_value_func=value_func_temp\n",
    "                    \n",
    "            diff=abs(value_func_old[s]-max_value_func)\n",
    "            delta=max(delta,diff)\n",
    "            value_func_new[s]=max_value_func\n",
    "\n",
    "        delta_collect[iteration] = delta\n",
    "        value_func_old = value_func_new\n",
    "        value_func_collect[:,iteration] = value_func_old\n",
    "        # Stopping criteria: STOP when the sup norm of (V_k-V_{k-1}) is less than some tolerance level(it's 1e-3 here).\n",
    "        if delta<=tol: break\n",
    "\n",
    "    temp=np.repeat(value_func_collect[:,iteration], iteration, axis=0)\n",
    "    temp=temp.reshape(16,iteration)\n",
    "    temp1 = abs(value_func_collect[:,0:iteration]-temp);\n",
    "    distance_from_converged_value_func = temp1.max(axis=0)\n",
    "\n",
    "    fig = plt.figure()\n",
    "    fig.suptitle(\"Value iteration convergence plots\", fontsize=16)\n",
    "    ax = plt.subplot(2,1,1)\n",
    "    ax.plot(range(1,iteration+1),delta_collect[0:iteration])\n",
    "    ax.set_title('||V_k-V_{k-1}|| plot')\n",
    "    ax.set_yscale('log')\n",
    "\n",
    "\n",
    "    ax = plt.subplot(2,1,2)\n",
    "    ax.plot(range(1,iteration+1),distance_from_converged_value_func)\n",
    "    ax.set_title('||V_k-V^*|| plot')\n",
    "    ax.set_yscale('log')\n",
    "\n",
    "    return value_func_new, iteration\n",
    "\n",
    "\n",
    "def value_function_to_policy(env, gamma, value_function):\n",
    "    \"\"\"\n",
    "    Mapping actions for each state using the value_function to get a policy\n",
    "        See section 4.4 of Reinforcement Learning: An Introduction (Adaptive Computation and Machine Learning) by Sutton and Barto\n",
    "    \"\"\"\n",
    "    policy=np.zeros(env.nS,dtype='int')\n",
    "    for s in range(env.nS):\n",
    "        max_value_func=-1\n",
    "        max_action=-1\n",
    "        for a in range(env.nA):\n",
    "            value_func_temp=0\n",
    "            for next_state_from_tpm in env.P[s][a]:\n",
    "                prob_action = next_state_from_tpm[0]\n",
    "                cur_reward = next_state_from_tpm[2]\n",
    "                future_reward = gamma * value_function[next_state_from_tpm[1]]\n",
    "                value_func_temp+=prob_action * (cur_reward + future_reward)\n",
    "            if value_func_temp>max_value_func:\n",
    "                max_value_func=value_func_temp\n",
    "                max_action=a\n",
    "        policy[s]=max_action\n",
    "\n",
    "    return policy\n",
    "\n",
    "\n",
    "\n",
    "print(\"\\nDoing Value Iteration\")\n",
    "start_time=time.time()\n",
    "value_function,value_iters=value_iteration(env,gamma)\n",
    "print(\"Total time taken: \"+str((time.time()-start_time)))\n",
    "\n",
    "print(\"Value function: \"+str(value_function))\n",
    "\n",
    "print(\"Total Value Iteration Steps: \"+str(value_iters))\n",
    "print(\"Policy:\")\n",
    "policy=value_function_to_policy(env,gamma,value_function)\n",
    "policy_str=print_policy(policy,action_names)\n",
    "\n",
    "f, ax = plt.subplots(figsize=(11, 9))\n",
    "cmap = seaborn.diverging_palette(220, 10, as_cmap=True)\n",
    "reshaped=np.reshape(value_function,(grid,grid))\n",
    "seaborn.heatmap(reshaped, cmap=cmap, vmax=1.1,\n",
    "            square=True, xticklabels=grid+1, yticklabels=grid+1,\n",
    "            linewidths=.5, cbar_kws={\"shrink\": .5}, ax=ax, annot=True, fmt=\"f\")\n",
    "counter=0\n",
    "for j in range(0, 4):\n",
    "    for i in range(0, 4):\n",
    "        if policy_str[counter]==\"DOWN\":\n",
    "            plt.text(i+0.5, j+0.7, u'\\u2193', fontsize=12)\n",
    "        elif policy_str[counter]==\"UP\":\n",
    "            plt.text(i+0.5, j+0.7, u'\\u2191', fontsize=12)\n",
    "        elif policy_str[counter]==\"LEFT\":\n",
    "            plt.text(i+0.5, j+0.7, u'\\u2190', fontsize=12)\n",
    "        else:\n",
    "            plt.text(i+0.5, j+0.7, u'\\u2192', fontsize=12)\n",
    "        counter=counter+1\n",
    "\n",
    "plt.title('Heatmap of policy iteration with value function values and directions')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Enter 'Y' if you want to see the final animation of the policy achieved. Else enter something else.\n",
      "y\n",
      "Final Policy Animation\n",
      "\n",
      "\u001b[41mS\u001b[0mFFF\n",
      "FHFH\n",
      "FFFH\n",
      "HFFG\n",
      "  (Down)\n",
      "SFFF\n",
      "\u001b[41mF\u001b[0mHFH\n",
      "FFFH\n",
      "HFFG\n",
      "  (Down)\n",
      "SFFF\n",
      "FHFH\n",
      "\u001b[41mF\u001b[0mFFH\n",
      "HFFG\n",
      "  (Right)\n",
      "SFFF\n",
      "FHFH\n",
      "F\u001b[41mF\u001b[0mFH\n",
      "HFFG\n",
      "  (Down)\n",
      "SFFF\n",
      "FHFH\n",
      "FFFH\n",
      "H\u001b[41mF\u001b[0mFG\n",
      "  (Right)\n",
      "SFFF\n",
      "FHFH\n",
      "FFFH\n",
      "HF\u001b[41mF\u001b[0mG\n",
      "  (Right)\n",
      "SFFF\n",
      "FHFH\n",
      "FFFH\n",
      "HFF\u001b[41mG\u001b[0m\n"
     ]
    }
   ],
   "source": [
    "########################################################################\n",
    "#################### Final policy animation ############################\n",
    "########################################################################\n",
    "\n",
    "flag=input(\"\\nEnter 'Y' if you want to see the final animation of the policy achieved. Else enter something else.\\n\")\n",
    "if flag==\"Y\" or flag==\"y\": print(\"Final Policy Animation\")\n",
    "def run_policy(env,gamma,policy):\n",
    "    initial_state = env.reset()\n",
    "    env.render()\n",
    "    current_state = initial_state\n",
    "    while True:\n",
    "        nextstate, reward, done, debug_info = env.step(policy[current_state])\n",
    "        env.render()\n",
    "\n",
    "        if done:\n",
    "            break\n",
    "\n",
    "        current_state=nextstate\n",
    "        time.sleep(1)\n",
    "\n",
    "if flag==\"Y\" or flag==\"y\": run_policy(env,gamma,policy)\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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