counterfactual_regret_minimization.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "ROCK = 0\n",
    "PAPER = 1\n",
    "SCISSORS = 2\n",
    "NUM_ACTIONS = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "regret_sum = np.zeros(NUM_ACTIONS)\n",
    "strategy = np.zeros(NUM_ACTIONS)\n",
    "strategy_sum = np.zeros(NUM_ACTIONS)\n",
    "opp_strategy = np.array([0.4, 0.3, 0.3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_strategy():\n",
    "    normalizing_sum = 0\n",
    "    for action in range(NUM_ACTIONS):\n",
    "        strategy[action] = regret_sum[action] if(regret_sum[action] > 0) else 0\n",
    "        normalizing_sum += strategy[action]\n",
    "    for action in range(NUM_ACTIONS):\n",
    "        if(normalizing_sum > 0):\n",
    "            strategy[action] /= normalizing_sum\n",
    "        else:\n",
    "            strategy[action] = 1 / NUM_ACTIONS\n",
    "        strategy_sum[action] += strategy[action]\n",
    "    return strategy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_action(strategy):\n",
    "    r = np.random.rand()\n",
    "    a = 0\n",
    "    cumulative_probability = 0\n",
    "    while a < NUM_ACTIONS - 1:\n",
    "        cumulative_probability += strategy[a]\n",
    "        if(r < cumulative_probability):\n",
    "            break\n",
    "        a += 1\n",
    "    return a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train(epochs=1000):\n",
    "    action_utility = np.zeros(NUM_ACTIONS)\n",
    "    win_rate = 0\n",
    "    output = [\n",
    "        [],\n",
    "        [],\n",
    "        []\n",
    "    ]\n",
    "    for i in range(epochs): \n",
    "        # Get regret-matched mixed-strategy actions\n",
    "        strategy = get_strategy()\n",
    "        my_action = get_action(strategy)\n",
    "        other_action = get_action(opp_strategy)\n",
    "    \n",
    "        # Compute action utilities\n",
    "        action_utility[other_action] = 0        \n",
    "        \n",
    "        state = (0 if(other_action == NUM_ACTIONS - 1) else other_action + 1)\n",
    "        \n",
    "        state1 = (NUM_ACTIONS - 1 if(other_action == 0) else other_action - 1)\n",
    "        \n",
    "        action_utility[state] = 1\n",
    "        action_utility[state1] = - 1\n",
    "        \n",
    "        # Accumulate action regrets\n",
    "        for action in range(NUM_ACTIONS):\n",
    "            regret_sum[action] += action_utility[action] - action_utility[my_action]\n",
    "            output[action].append(regret_sum[action])\n",
    "            \n",
    "    plt.plot(output[0])\n",
    "    plt.plot(output[2])\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_average_strategy():\n",
    "    average_strategy = np.zeros(NUM_ACTIONS)\n",
    "    normalizing_sum = 0\n",
    "    for action in range(NUM_ACTIONS):\n",
    "        normalizing_sum += strategy_sum[action]\n",
    "    for action in range(NUM_ACTIONS):\n",
    "        if(normalizing_sum > 0):\n",
    "            average_strategy[action] = strategy_sum[action] / normalizing_sum\n",
    "        else:\n",
    "            average_strategy[action] = 1.0 / NUM_ACTIONS\n",
    "    return average_strategy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7afd95f828>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "OK\n"
     ]
    }
   ],
   "source": [
    "train()\n",
    "print(\"OK\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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wQ6tqsqqWAbcAT5llv0Oqbo7+5cBzk/zCPNR5jzPki8OOBycCb+l/QfcBO+mmWb4L/A2wPcmdwPeB8wfuG+A1Sd5ON/L4Pl2AU1Wbk5wCfCJJ0X1I+pyq+up4YVX1wyR/RzdS3AC8McnJwJ1000AvHt9HM6uq65PcAKypqkv6y0jfkmQj3dUwlwD/0Pe9McnLgUv7+dyiuzJm/JhvS/IQYHOSp1fVnXfbCzo+rKW7am3U++k+ED/Udyvun67Z751V9ebRDlX11SSX0l3IcOF8FHtP4h2qktQgp2UkqUGGuyQ1yHCXpAYZ7pLUIMNdkhpkuEtSgwx3SWqQ4S5JDfp/IE73WCkkPTQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7afb5a2da0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "strategy = get_average_strategy()\n",
    "D = {\n",
    "    \"ROCK\":strategy[0],\n",
    "    \"PAPER\":strategy[1],\n",
    "    \"SCISSORS\":strategy[2]\n",
    "}\n",
    "\n",
    "plt.bar(range(len(D)), list(D.values()), align='center')\n",
    "plt.xticks(range(len(D)), list(D.keys()))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# http://modelai.gettysburg.edu/2013/cfr/cfr.pdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}