{
 "metadata": {
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  },
  "orig_nbformat": 2,
  "kernelspec": {
   "name": "python3",
   "display_name": "Python 3.7.0 64-bit ('3.7')"
  },
  "interpreter": {
   "hash": "70b38d7a306a849643e446cd70466270a13445e5987dfa1344ef2b127438fa4d"
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 },
 "nbformat": 4,
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 "cells": [
  {
   "source": [
    "# Peter and the Wolf: Realistic Environment\n",
    "\n",
    "In our situation, Peter was able to move around almost without getting tired or hungry. In more realistic world, we has to sit down and rest from time to time, and also to feed himself. Let's make our world more realistic, by implementing the following rules:\n",
    "\n",
    "1. By moving from one place to another, Peter loses **energy** and gains some **fatigue**.\n",
    "2. Peter can gain more energy by eating apples.\n",
    "3. Peter can get rid of fatigue by resting under the tree or on the grass (i.e. walking into a board location with a tree or grass - green field)\n",
    "4. Peter needs to find and kill the wolf\n",
    "5. In order to kill the wolf, Peter needs to have certain levels of energy and fatigue, otherwise he loses the battle.\n"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import random\n",
    "import math\n",
    "from rlboard import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "width, height = 8,8\n",
    "m = Board(width,height)\n",
    "m.randomize(seed=13)\n",
    "m.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "actions = { \"U\" : (0,-1), \"D\" : (0,1), \"L\" : (-1,0), \"R\" : (1,0) }\n",
    "action_idx = { a : i for i,a in enumerate(actions.keys()) }"
   ]
  },
  {
   "source": [
    "## Defining state\n",
    "\n",
    "In our new game rules, we need to keep track of energy and fatigue at each board state. Thus we will create an object `state` that will carry all required information about current problem state, including state of the board, current levels of energy and fatigue, and whether we can win the wolf while at terminal state:"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "class state:\n",
    "    def __init__(self,board,energy=10,fatigue=0,init=True):\n",
    "        self.board = board\n",
    "        self.energy = energy\n",
    "        self.fatigue = fatigue\n",
    "        self.dead = False\n",
    "        if init:\n",
    "            self.board.random_start()\n",
    "        self.update()\n",
    "\n",
    "    def at(self):\n",
    "        return self.board.at()\n",
    "\n",
    "    def update(self):\n",
    "        if self.at() == Board.Cell.water:\n",
    "            self.dead = True\n",
    "            return\n",
    "        if self.at() == Board.Cell.tree:\n",
    "            self.fatigue = 0\n",
    "        if self.at() == Board.Cell.apple:\n",
    "            self.energy = 10\n",
    "\n",
    "    def move(self,a):\n",
    "        self.board.move(a)\n",
    "        self.energy -= 1\n",
    "        self.fatigue += 1\n",
    "        self.update()\n",
    "\n",
    "    def is_winning(self):\n",
    "        return self.energy > self.fatigue"
   ]
  },
  {
   "source": [
    "Let's try to solve the problem using random walk and see if we succeed:"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "metadata": {},
     "execution_count": 5
    }
   ],
   "source": [
    "def random_policy(state):\n",
    "    return random.choice(list(actions))\n",
    "\n",
    "def walk(board,policy):\n",
    "    n = 0 # number of steps\n",
    "    s = state(board)\n",
    "    while True:\n",
    "        if s.at() == Board.Cell.wolf:\n",
    "            if s.is_winning():\n",
    "                return n # success!\n",
    "            else:\n",
    "                return -n # failure!\n",
    "        if s.at() == Board.Cell.water:\n",
    "            return 0 # died\n",
    "        a = actions[policy(m)]\n",
    "        s.move(a)\n",
    "        n+=1\n",
    "\n",
    "walk(m,random_policy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Killed by wolf = 5, won: 1 times, drown: 94 times\n"
     ]
    }
   ],
   "source": [
    "def print_statistics(policy):\n",
    "    s,w,n = 0,0,0\n",
    "    for _ in range(100):\n",
    "        z = walk(m,policy)\n",
    "        if z<0:\n",
    "            w+=1\n",
    "        elif z==0:\n",
    "            n+=1\n",
    "        else:\n",
    "            s+=1\n",
    "    print(f\"Killed by wolf = {w}, won: {s} times, drown: {n} times\")\n",
    "\n",
    "print_statistics(random_policy)"
   ]
  },
  {
   "source": [
    "## Reward Function\n"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def reward(s):\n",
    "    r = s.energy-s.fatigue\n",
    "    if s.at()==Board.Cell.wolf:\n",
    "        return 100 if s.is_winning() else -100\n",
    "    if s.at()==Board.Cell.water:\n",
    "        return -100\n",
    "    return r"
   ]
  },
  {
   "source": [
    "## Q-Learning algorithm\n",
    "\n",
    "The actual learning algorithm stays pretty much unchanged, we just use `state` instead of just board position."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "Q = np.ones((width,height,len(actions)),dtype=np.float)*1.0/len(actions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def probs(v,eps=1e-4):\n",
    "    v = v-v.min()+eps\n",
    "    v = v/v.sum()\n",
    "    return v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      ""
     ]
    }
   ],
   "source": [
    "\n",
    "from IPython.display import clear_output\n",
    "\n",
    "lpath = []\n",
    "\n",
    "for epoch in range(10000):\n",
    "    clear_output(wait=True)\n",
    "    print(f\"Epoch = {epoch}\",end='')\n",
    "\n",
    "    # Pick initial point\n",
    "    s = state(m)\n",
    "    \n",
    "    # Start travelling\n",
    "    n=0\n",
    "    cum_reward = 0\n",
    "    while True:\n",
    "        x,y = s.board.human\n",
    "        v = probs(Q[x,y])\n",
    "        while True:\n",
    "            a = random.choices(list(actions),weights=v)[0]\n",
    "            dpos = actions[a]\n",
    "            if s.board.is_valid(s.board.move_pos(s.board.human,dpos)):\n",
    "                break \n",
    "        s.move(dpos)\n",
    "        r = reward(s)\n",
    "        if abs(r)==100: # end of game\n",
    "            print(f\" {n} steps\",end='\\r')\n",
    "            lpath.append(n)\n",
    "            break\n",
    "        alpha = np.exp(-n / 3000)\n",
    "        gamma = 0.5\n",
    "        ai = action_idx[a]\n",
    "        Q[x,y,ai] = (1 - alpha) * Q[x,y,ai] + alpha * (r + gamma * Q[x+dpos[0], y+dpos[1]].max())\n",
    "        n+=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "m.plot(Q)"
   ]
  },
  {
   "source": [
    "## Results\n",
    "\n",
    "Let's see if we were successful training Peter to fight the wolf!"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Killed by wolf = 1, won: 9 times, drown: 90 times\n"
     ]
    }
   ],
   "source": [
    "def qpolicy(m):\n",
    "        x,y = m.human\n",
    "        v = probs(Q[x,y])\n",
    "        a = random.choices(list(actions),weights=v)[0]\n",
    "        return a\n",
    "\n",
    "print_statistics(qpolicy)"
   ]
  },
  {
   "source": [
    "We now see much less cases of drowning, but Peter is still not always able to kill the wolf. Try to experiment and see if you can improve this result by playing with hyperparameters."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fe0987e7dd8>]"
      ]
     },
     "metadata": {},
     "execution_count": 13
    },
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.plot(lpath)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ]
}