MLA_2.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "MLA_2.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyP/ha7n8CF2U/Iihx8K2NN0",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/AlexHudnev/mla/blob/main/MLA_2.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VKtvi8BbvWzw"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import random as random\n",
        "\n",
        "class CoinBetGame:\n",
        "  def __init__(self, p_heads, theta=0.0001):\n",
        "        self.p_heads = p_heads\n",
        "        self.theta = theta\n",
        "        self.rewards = np.zeros(101)\n",
        "        self.rewards[100] = 1\n",
        "        self.V = np.zeros(101)\n",
        "\n",
        "  def lookahead(self, s):\n",
        "        A = np.zeros(101)\n",
        "        stakes = range(1, min(s, 100-s)+1)\n",
        "        for a in stakes:\n",
        "            A[a] = self.p_heads * (self.rewards[s+a] + self.V[s+a])\\\n",
        "             + (1-self.p_heads) * (self.rewards[s-a] + self.V[s-a])\n",
        "        return A\n",
        "\n",
        "  def execute(self):\n",
        "     while True:\n",
        "        delta = 0\n",
        "        for s in range(1, 100):\n",
        "            A = self.lookahead(s)\n",
        "            best_action_value = np.max(A)\n",
        "            delta = max(delta, np.abs(best_action_value - self.V[s]))\n",
        "            self.V[s] = best_action_value        \n",
        "\n",
        "        if delta < self.theta:\n",
        "            break\n",
        "     policy = np.zeros(100)\n",
        "     for s in range(1, 100):\n",
        "         A = self.lookahead(s)\n",
        "         best_action = np.argmax(A)\n",
        "         policy[s] = best_action\n",
        "    \n",
        "     return policy, self.V\n",
        "\n",
        "class CoinBetGameModified(CoinBetGame):\n",
        "  def __init__(self, p_heads, theta=0.0001):\n",
        "        super(CoinBetGameModified, self ).__init__(p_heads, theta)\n",
        "        self.rewards = np.ones(101)*-0.0001\n",
        "        self.rewards[100] = 1\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "lVaTtmMEvfeL",
        "outputId": "46c30f25-85e4-4c06-a4ce-5ec39353f12d"
      },
      "source": [
        "bet_game = CoinBetGame(0.25)\n",
        "policy, v = bet_game.execute()\n",
        "\n",
        "print(\"\")\n",
        "print(\"P head: 0.25\")\n",
        "print(\"\")\n",
        "\n",
        "x = range(100)\n",
        "y = policy\n",
        "plt.bar(x, y, align='center', alpha=0.5)\n",
        "plt.xlabel('Capital')\n",
        "plt.ylabel('Policy')\n",
        "plt.show()\n",
        "\n",
        "bet_game_modified = CoinBetGameModified(0.25)\n",
        "policy1, v1 = bet_game_modified.execute()\n",
        "\n",
        "y = policy1\n",
        "plt.bar(x, y, align='center', alpha=0.5)\n",
        "plt.title('Modified')\n",
        "plt.xlabel('Capital')\n",
        "plt.ylabel('Policy')\n",
        "plt.show()\n",
        "\n",
        "\n",
        "y = policy\n",
        "y1 = policy1\n",
        "plt.bar(x, y, align='center', alpha=0.5)\n",
        "plt.bar(x, y1, align='center', alpha=0.5)\n",
        "plt.title('Modified vs Standart')\n",
        "plt.xlabel('Capital')\n",
        "plt.ylabel('Policy')\n",
        "plt.show()\n",
        "\n",
        "y = v[:100]\n",
        "y1 = v1[:100]\n",
        "plt.bar(x, y, align='center', alpha=0.5)\n",
        "plt.bar(x, y1, align='center', alpha=0.5)\n",
        "plt.title('Modified vs Standart')\n",
        "plt.xlabel('Capital')\n",
        "plt.ylabel('V')\n",
        "plt.show()\n",
        "\n",
        "\n",
        "\n",
        "bet_game = CoinBetGame(0.5)\n",
        "policy, v = bet_game.execute()\n",
        "\n",
        "print(\"\")\n",
        "print(\"P head: 0.5\")\n",
        "print(\"\")\n",
        "\n",
        "x = range(100)\n",
        "y = policy\n",
        "plt.bar(x, y, align='center', alpha=0.5)\n",
        "plt.xlabel('Capital')\n",
        "plt.ylabel('Policy')\n",
        "plt.show()\n",
        "\n",
        "bet_game_modified = CoinBetGameModified(0.5)\n",
        "policy1, v1 = bet_game_modified.execute()\n",
        "\n",
        "\n",
        "x = range(100)\n",
        "y = policy1\n",
        "plt.bar(x, y, align='center', alpha=0.5)\n",
        "plt.title('Modified')\n",
        "plt.xlabel('Capital')\n",
        "plt.ylabel('Policy')\n",
        "plt.show()\n",
        "\n",
        "x = range(100)\n",
        "y = policy\n",
        "y1 = policy1\n",
        "plt.bar(x, y, align='center', alpha=0.5)\n",
        "plt.bar(x, y1, align='center', alpha=0.5)\n",
        "plt.title('Modified vs Standart')\n",
        "plt.xlabel('Capital')\n",
        "plt.ylabel('Policy')\n",
        "plt.show()\n",
        "\n",
        "y = v[:100]\n",
        "y1 = v1[:100]\n",
        "plt.bar(x, y, align='center', alpha=0.5)\n",
        "plt.bar(x, y1, align='center', alpha=0.5)\n",
        "plt.title('Modified vs Standart')\n",
        "plt.xlabel('Capital')\n",
        "plt.ylabel('V')\n",
        "plt.show()\n",
        "\n",
        "bet_game = CoinBetGame(0.55)\n",
        "policy, v = bet_game.execute()\n",
        "\n",
        "print(\"\")\n",
        "print(\"P head: 0.55\")\n",
        "print(\"\")\n",
        "\n",
        "x = range(100)\n",
        "y = policy\n",
        "plt.bar(x, y, align='center', alpha=0.5)\n",
        "plt.xlabel('Capital')\n",
        "plt.ylabel('Policy')\n",
        "plt.show()\n",
        "\n",
        "\n",
        "bet_game_modified = CoinBetGameModified(0.55)\n",
        "policy1, v1 = bet_game_modified.execute()\n",
        "\n",
        "\n",
        "\n",
        "x = range(100)\n",
        "y = policy1\n",
        "plt.bar(x, y, align='center', alpha=0.5)\n",
        "plt.title('Modified')\n",
        "plt.xlabel('Capital')\n",
        "plt.ylabel('Policy')\n",
        "plt.show()\n",
        "\n",
        "x = range(100)\n",
        "y = policy\n",
        "y1 = policy1\n",
        "plt.bar(x, y, align='center', alpha=0.5)\n",
        "plt.bar(x, y1, align='center', alpha=0.5)\n",
        "plt.title('Modified vs Standart')\n",
        "plt.xlabel('Capital')\n",
        "plt.ylabel('Policy')\n",
        "plt.show()\n",
        "\n",
        "y = v[:100]\n",
        "y1 = v1[:100]\n",
        "plt.bar(x, y, align='center', alpha=0.5)\n",
        "plt.bar(x, y1, align='center', alpha=0.5)\n",
        "plt.title('Modified vs Standart')\n",
        "plt.xlabel('Capital')\n",
        "plt.ylabel('V')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\n",
            "P head: 0.25\n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "P head: 0.5\n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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9hmqDJGlLQ0Y999MN6nY4cDTwuiSHAycDF1TVocAF/bQkaZEMVviralNVfa9/fjdwFbA/cALd4G/0P08cqg2SpC0tysXdJCuBpwKXAPtW1aZ+0S3AvrO85qQkG5Js2Lx582I0c2JcfPrbzPY1qIs33v5Atr+o1p/yYOavbTZ44U+yG92Xt7y5qu4aXVZVBdRMr6uq06pqVVWtWrFixdDNlKRmDFr4kzySruifWVVf7mf/PMl+/fL9gFuHbIMk6aGGvKsnwOnAVVX1/pFF5wJr+udrgHOGaoMkaUtD3sf/DODVwA+TfL+f907gPcBZSdYCNwAvGbANzZjK9FevPXXMLdEkGs3zB7tff75Gs37v8Z+XwQp/VX2Lbtz+mTx7qP1Kkh6eQzZIUmMs/JLUGMfqWcbM9TWksdynv63M++fFHr8kNcbCL0mNsfBLUmPM+JcZc30NaSnm+vMe79+8f6vs8UtSYyz8ktQYC78kNcbCL0mN8eLuMuAFXQ1pKV7QXTBe6J2RPX5JaoyFX5IaY+GXpMaY8S9R5voa0kTn+rMx73+APX5JaoyFX5IaY+GXpMaY8S8h5voaUpO5/mwaz/vt8UtSYyz8ktQYC78kNcaMf8zM9aUxazDvt8cvSY2x8EtSYyz8ktQYM/4xMNeXlo7Rzzespo283x6/JDXGwi9JjbHwS1JjzPgXibm+tHTMadyiCb6/f7Aef5Izktya5Ecj8/ZOcn6Sa/qfew21f0nSzIaMej4JPHfavJOBC6rqUOCCflqStIgGK/xVdRHwi2mzTwDW9c/XAScOtX9J0swWO+Pft6o29c9vAfadbcUkJwEnARx44IGL0LSFZ64vLR3b/X0EU5n/BOT9Y7urp6oKqIdZflpVraqqVStWrFjElknSZFvswv/zJPsB9D9vXeT9S1LzFrvwnwus6Z+vAc5Z5P1LUvOGvJ3zc8DFwGFJbkqyFngP8Jwk1wDH9dOSpEU02MXdqnr5LIuePdQ+x23qYi54QVdaChbyC+antrX6GJb9hV6HbJCkxlj4JakxFn5JaoyDtG2n0Vxf0vgtZK4/J8sw77fHL0mNsfBLUmMs/JLUGDP+bWCuL43HQ+6ln2H+2C2TvN8evyQ1xsIvSY2x8EtSY8z458hcX1palkyuP2K5jOdjj1+SGmPhl6TGWPglqTFm/A/DXF/S1mztswVLMe+3xy9JjbHwS1JjLPyS1Bgz/mnM9aXxmC0rX4q2q61LIO+3xy9JjbHwS1JjLPyS1Bgzfsz1paVmOeX9czF6PEvh/n57/JLUGAu/JDXGwi9JjbHwS1Jjmr246wVdafyW8kXc0S96WYz2TdWk1WtPHXxf9vglqTEWfklqjIVfkhrTVMZvrq/WLMUvJF/KFvv3NeuXuAyc94+lx5/kuUl+nOTaJCePow2S1KpFL/xJdgD+K3A8cDjw8iSHL3Y7JKlV4+jxHwVcW1Ubq+o3wOeBE8bQDklqUqpqcXeYvBh4blW9tp9+NfDHVfX6aeudBJzUTx4G/Hg7drsPcNt2vH458pjb4DG3YVuP+aCqWjF95pK9uFtVpwGnLcS2kmyoqlULsa3lwmNug8fchoU+5nFEPTcDTxiZPqCfJ0laBOMo/N8FDk1ycJJHAS8Dzh1DOySpSYse9VTV/UleD3wd2AE4o6quGHi3CxIZLTMecxs85jYs6DEv+sVdSdJ4OWSDJDXGwi9JjZn4wt/C8BBJnpBkfZIrk1yR5E39/L2TnJ/kmv7nXuNu60JKskOSy5Kc108fnOSS/lx/ob95YKIk2TPJ2UmuTnJVktUNnOd/3/+7/lGSzyXZadLOdZIzktya5Ecj82Y8r+l8uD/2y5M8bb77m+jC39DwEPcDb62qw4Gjgdf1x3kycEFVHQpc0E9PkjcBV41Mvxf4QFUdAtwBrB1Lq4b1IeBrVfUk4Ai645/Y85xkf+CNwKqqegrdDSEvY/LO9SeB506bN9t5PR44tH+cBHxkvjub6MJPI8NDVNWmqvpe//xuumKwP92xrutXWwecOJ4WLrwkBwDPBz7eTwc4Fji7X2WijhcgyWOAPwFOB6iq31TVnUzwee7tCOycZEdgF2ATE3auq+oi4BfTZs92Xk8APlWdbwN7JtlvPvub9MK/P3DjyPRN/byJlWQl8FTgEmDfqtrUL7oF2HdMzRrCB4G/BH7XTz8WuLOq7u+nJ/FcHwxsBj7RR1wfT7IrE3yeq+pm4FTgZ3QF/5+AS5n8cw2zn9ftrmuTXvibkmQ34EvAm6vqrtFl1d23OxH37iZ5AXBrVV067rYssh2BpwEfqaqnAr9kWqwzSecZoM+1T6D7o/d4YFe2jEQm3kKf10kv/M0MD5HkkXRF/8yq+nI/++dTbwH7n7eOq30L7BnAC5NcTxffHUuXfe/ZxwEwmef6JuCmqrqknz6b7g/BpJ5ngOOAn1bV5qq6D/gy3fmf9HMNs5/X7a5rk174mxgeos+3Tweuqqr3jyw6F1jTP18DnLPYbRtCVb2jqg6oqpV05/SbVfVKYD3w4n61iTneKVV1C3BjksP6Wc8GrmRCz3PvZ8DRSXbp/51PHfNEn+vebOf1XOA1/d09RwP/NBIJzU1VTfQDeB7wE+A64K/G3Z6BjvGZdG8DLwe+3z+eR5d7XwBcA/wvYO9xt3WAY38WcF7//PeB7wDXAl8EHj3u9g1wvEcCG/pz/VVgr0k/z8C7gauBHwGfBh49aeca+BzdNYz76N7ZrZ3tvAKhu1vxOuCHdHc8zWt/DtkgSY2Z9KhHkjSNhV+SGmPhl6TGWPglqTEWfklqjIVfTUvye0k+n+S6JJcm+YckT9yG7Xx8agDAJO+c42uuT7LPfPclbS9v51Sz+g8E/R9gXVX9937eEcAeVfW/t2O791TVbnNY73q6e7Bv29Z9SdvCHr9adgxw31TRB6iqHwCXJbkgyfeS/DDJCdANgNePg39mPxb+2Ul26ZddmGRVkvfQjST5/SRn9su+2r+buCLJSWM4TukhLPxq2VPoRnqc7v8BL6qqp9H9cXhf/+4A4DDgv1XVHwB3Af9u9IVVdTLwq6o6srphJAD+vKqeDqwC3pjksQMcizRnFn5pSwH+LsnldB+V358Hh8S9sar+sX/+GbrhMrbmjUl+AHybbnCtQxe4vdK87Lj1VaSJdQUPDvQ16pXACuDpVXVfn8Xv1C+bflHsYS+SJXkW3QiTq6vq3iQXjmxLGgt7/GrZN4FHj+buSf45cBDdeP/3JTmmn55yYJLV/fNXAN+aYbv39cNkAzwGuKMv+k+i+2pMaaws/GpWdbe0vQg4rr+d8wrgFOAfgFVJfgi8hm5kyCk/pvtO46voRsac6ftOTwMu7y/ufg3YsV//PXRxjzRW3s4pzVH/tZbnVfel39KyZY9fkhpjj1+SGmOPX5IaY+GXpMZY+CWpMRZ+SWqMhV+SGvP/AbJU0j51SQHoAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n",
            "P head: 0.55\n",
            "\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}