FrozenLake_Mellowmax_vs_Boltzmann.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "FrozenLake-Mellowmax-vs-Boltzmann.ipynb",
      "version": "0.3.2",
      "provenance": [],
      "collapsed_sections": [],
      "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/sayam47/Mellowmax-RL/blob/master/FrozenLake_Mellowmax_vs_Boltzmann.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zidIrI3qYPcQ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from collections import deque\n",
        "from collections import defaultdict\n",
        "import gym\n",
        "import sys\n",
        "import math\n",
        "import numpy as np\n",
        "import warnings\n",
        "warnings.filterwarnings('ignore')\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xtjqSSs8YV9F",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def interact(env, agent, num_episodes=5000, window=100):\n",
        "    avg_rewards = deque(maxlen=num_episodes)\n",
        "    best_avg_reward = -math.inf\n",
        "    samp_rewards = deque(maxlen=window)\n",
        "    for i_episode in range(1, num_episodes+1):\n",
        "        state = env.reset() #initialize the environment\n",
        "        samp_reward = 0\n",
        "        while True:\n",
        "            action = agent.select_action(state)\n",
        "            next_state, reward, done, _ = env.step(action)\n",
        "            agent.step(state, action, reward, next_state, done)\n",
        "            samp_reward += reward\n",
        "            state = next_state\n",
        "#             print(\"\\rRewards : {}\".format(samp_reward),end=\"\")\n",
        "            if done:\n",
        "                samp_rewards.append(samp_reward)\n",
        "                break\n",
        "        \n",
        "        avg_reward=0\n",
        "        if (i_episode >= 100):\n",
        "            avg_reward = np.mean(samp_rewards)\n",
        "            avg_rewards.append(avg_reward)\n",
        "            if avg_reward > best_avg_reward:\n",
        "                best_avg_reward = avg_reward\n",
        "        averages_history.append(samp_reward)\n",
        "        if samp_reward >= 1:\n",
        "#             print('\\nEnvironment solved in {} episodes.'.format(i_episode), end=\"\")\n",
        "            return i_episode\n",
        "            break\n",
        "#         if i_episode == num_episodes: print('\\n')\n",
        "    return 10000"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2li2MDPKYaEK",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from scipy.optimize import brentq\n",
        "\n",
        "class Agent:\n",
        "\n",
        "    def __init__(self, nA=4,omega=25,beta=1,mellow=0):\n",
        "        self.mellow=mellow\n",
        "        self.beta=beta\n",
        "        self.nA = nA\n",
        "        self.omega=omega\n",
        "        self.Q = defaultdict(lambda: np.zeros(self.nA))\n",
        "        self.epsilon_function = None;\n",
        "        self.next_value_function = None;\n",
        "        self.gamma = 0.9\n",
        "        self.alpha = 0.1\n",
        "           \n",
        "    def mellowmax(self,beta,state):\n",
        "        c=np.max(self.Q[state])\n",
        "        mellow=c+np.log(np.sum(np.exp(self.omega*(self.Q[state]-c)))/self.nA)/self.omega\n",
        "        ans=np.sum(np.exp((self.Q[state]-mellow)*beta)*(self.Q[state]-mellow))\n",
        "        return ans\n",
        "\n",
        "    def get_action_probability(self, state):\n",
        "        if self.mellow==1:\n",
        "            beta=brentq(self.mellowmax,-500,500,args=(state,))\n",
        "        else:\n",
        "            beta=self.beta\n",
        "        policy_s = np.exp(beta*self.Q[state])/np.sum(np.exp(beta*self.Q[state]))\n",
        "        return policy_s\n",
        "\n",
        "    def select_action(self, state):\n",
        "        policy_s = self.get_action_probability(state)\n",
        "        return np.random.choice(np.arange(self.nA), p=policy_s)\n",
        "    \n",
        "    def step(self, state, action, reward, next_state, done):\n",
        "        next_action_value = self.Q[next_state][self.select_action(next_state)]\n",
        "        self.Q[state][action] += self.alpha * (reward  + self.gamma * next_action_value - self.Q[state][action])"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EMm3wryCYdpH",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "env = gym.make('FrozenLake-v0')\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_La_u0xbYe_k",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZscPTNg9YhIf",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "iteration = 50\n",
        "his_b=[] #history_of_values\n",
        "solve_his_b=[]\n",
        "for i in range(1,31):\n",
        "    b=0\n",
        "    for j in range(iteration):\n",
        "        averages_history=[]\n",
        "        agent = Agent(beta=i)\n",
        "        sol=interact(env,agent)\n",
        "        b+=sol\n",
        "    b/=iteration\n",
        "    solve_his_b.append(b)\n",
        "#         his.append(averages_history)\n",
        "    "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RRoXjaRbYk9M",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "iteration=50\n",
        "his_m=[]\n",
        "solve_his_m=[]\n",
        "for i in range(1,31):\n",
        "    b=0\n",
        "    for j in range(iteration):\n",
        "        averages_history=[]\n",
        "        agent = Agent(omega=i,mellow=1)\n",
        "        sol=interact(env,agent)\n",
        "        b+=sol\n",
        "    b/=iteration\n",
        "    solve_his_m.append(b)\n",
        "#         his.append(averages_history)\n",
        "    "
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5tb7Y1lZYoyg",
        "colab_type": "code",
        "outputId": "4de6e445-b2b5-46c7-f371-697d1eabeab4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        }
      },
      "source": [
        "fig_best=plt.figure()\n",
        "ax=fig_best.add_subplot(111)\n",
        "plt.plot(np.arange(1,31),solve_his_b,label='boltzmaan')\n",
        "plt.plot(np.arange(1,31),solve_his_m,label='mellowmax')\n",
        "plt.xlabel('omega/beta')\n",
        "plt.ylabel('number of iterations')\n",
        "plt.ylim(0,100)\n",
        "plt.legend()\n",
        "plt.savefig('lake.png')"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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43+RX0dLu5vBCTxXXvjhrICw9EIeON5JTWsdVc+IRQhAT4scdSyay5oElGGOmc1ZQJesP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\nsQ/vkwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}