q_learning_totorial.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tutorial Simon Tamayo GIT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import math\n",
    "import pandas as pd\n",
    "np.set_printoptions(precision=4, suppress=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load initlial matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Adjacency matrix is:\n",
      "[[0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0]\n",
      " [1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1]\n",
      " [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1]]\n",
      "Reward matrix is:\n",
      "[[ -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1]\n",
      " [ -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1]\n",
      " [ -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1]\n",
      " [ -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1]\n",
      " [ -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1]\n",
      " [ -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1]\n",
      " [ -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1]\n",
      " [ -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1]\n",
      " [ -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1]\n",
      " [ -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1]\n",
      " [ -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1]\n",
      " [ -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1]\n",
      " [ -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1]\n",
      " [ -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1]\n",
      " [ -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1]\n",
      " [ -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1]\n",
      " [ -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1 100]\n",
      " [ -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1  -1 100]]\n"
     ]
    }
   ],
   "source": [
    "# Adjacency matrix (the graph of the problem)\n",
    "adj_mat = pd.read_csv('./adjacency_matrix.csv',sep=';',index_col=0).values\n",
    "print('Adjacency matrix is:')\n",
    "print(adj_mat)\n",
    "\n",
    "# Reward matrix\n",
    "reward_mat = pd.read_csv('./reward_matrix.csv',sep=';',index_col=0).values\n",
    "print('Reward matrix is:')\n",
    "print(reward_mat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initialize Q matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Q matrix (initial) is :\n",
      "[[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "# The Q matrix is the memory of the learner and it maps actions to states\n",
    "nbOfStates = len(reward_mat)\n",
    "states = np.arange(nbOfStates)\n",
    "Q = np.zeros([nbOfStates,nbOfStates])\n",
    "print('Q matrix (initial) is :')\n",
    "print(Q)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Q Learning algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--------------------\n",
      "[[ 0.      0.0099  0.      0.      0.      0.0099  0.      0.      0.\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.0099  0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.0099  0.      0.0099  0.      0.      0.0099  0.      0.\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.0099  0.      0.      0.      0.\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.0099  0.      0.      0.      0.0099  0.\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.0099  0.      0.      0.      0.      0.      0.      0.      0.0099\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.0099  0.      0.      0.      0.      0.      0.\n",
      "   0.0099  0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.0099  0.      0.      0.\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.0099  0.      0.\n",
      "   0.      0.0099  0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.0099  0.      0.      0.0099  0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.      0.0099  0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.0099  0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.      0.      0.     -0.9911  0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.      0.      0.0099  0.      0.0099  0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.0099  0.      0.      0.      0.0099  0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.      0.0099  0.      0.      0.      0.      0.0099]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.0099  1.    ]]\n",
      "--------------------\n",
      "[[ 0.      0.0099  0.      0.      0.      0.0099  0.      0.      0.\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.0099  0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.0099  0.      0.0099  0.      0.      0.0099  0.      0.\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.0099  0.      0.      0.      0.\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.0099  0.      0.      0.      0.0099  0.\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.0099  0.      0.      0.      0.      0.      0.      0.      0.0099\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.0099  0.      0.      0.      0.      0.      0.\n",
      "   0.0099  0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.0099  0.      0.      0.\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.0099  0.      0.\n",
      "   0.      0.0099  0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.0099  0.      0.      0.0099  0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.      0.0099  0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.0099  0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.      0.      0.     -0.9911  0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.      0.      0.0099  0.      0.0099  0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.     -0.9911  0.      0.      0.      0.0099  0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.      0.0099  0.      0.      0.      0.      0.0099]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.0099  1.    ]]\n",
      "--------------------\n",
      "[[ 0.      0.0099  0.      0.      0.      0.0099  0.      0.      0.\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.0099  0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.0099  0.      0.0099  0.      0.      0.0099  0.      0.\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.     -0.9911  0.      0.0099  0.      0.      0.      0.\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.0099  0.      0.      0.      0.0099  0.\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.0099  0.      0.      0.      0.      0.      0.      0.      0.0099\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.0099  0.      0.      0.      0.      0.      0.\n",
      "   0.0099  0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.0099  0.      0.      0.\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.0099  0.      0.\n",
      "   0.      0.0099  0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.0099  0.      0.      0.0099  0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.      0.0099  0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.0099  0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.      0.      0.     -0.9911  0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.      0.      0.0099  0.      0.0099  0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.     -0.9911  0.      0.      0.      0.0099  0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.      0.0099  0.      0.      0.      0.      0.0099]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.0099  1.    ]]\n",
      "--------------------\n",
      "[[ 0.      0.0099  0.      0.      0.      0.0099  0.      0.      0.\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.0099  0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.0099  0.      0.0099  0.      0.     -0.9911  0.      0.\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.     -0.9911  0.      0.0099  0.      0.      0.      0.\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.0099  0.      0.      0.      0.0099  0.\n",
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      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.0099  0.      0.      0.\n",
      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.0099  0.      0.\n",
      "   0.      0.0099  0.      0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.0099  0.      0.      0.0099  0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.      0.0099  0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.0099  0.      0.      0.      0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
      "   0.      0.      0.      0.      0.     -0.9911  0.      0.      0.    ]\n",
      " [ 0.      0.      0.      0.      0.      0.      0.      0.      0.\n",
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      "   0.      0.      0.      0.      0.      0.      0.      0.0099  1.    ]]\n",
      "--------------------\n",
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      "   0.      0.      0.      0.      0.      0.      0.      0.      0.    ]\n",
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      "   0.      0.      0.      0.      0.0099  0.      0.0099  0.      0.    ]\n",
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      "   0.      0.      0.      0.0099  0.      0.      0.      0.      0.0099]\n",
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      "   0.      0.      0.      0.      0.      0.      0.      0.0099  1.    ]]\n",
      "--------------------\n",
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      "    0.       0.       0.       0.       0.0099   0.       0.       0.\n",
      "    0.     100.9   ]\n",
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      "    0.       0.       0.       0.       0.       0.       0.       0.\n",
      "    0.0099   1.    ]]\n",
      "--------------------\n",
      "[[  0.       0.0099   0.       0.       0.      -0.9911   0.       0.\n",
      "    0.       0.       0.       0.       0.       0.       0.       0.\n",
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      "    0.       0.      -0.9911   0.       0.       0.       0.0099   0.\n",
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      "    0.       0.       0.       0.       0.0099   0.       0.       0.\n",
      "    0.     100.9   ]\n",
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      "    0.       0.       0.       0.       0.       0.       0.       0.\n",
      "    0.0099   1.    ]]\n",
      "--------------------\n",
      "[[  0.       0.0099   0.       0.       0.      -0.9911   0.       0.\n",
      "    0.       0.       0.       0.       0.       0.       0.       0.\n",
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      "    0.     100.9   ]\n",
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      "    0.       0.       0.       0.       0.       0.       0.       0.\n",
      "    0.0099   1.    ]]\n",
      "--------------------\n",
      "[[  0.       0.0099   0.       0.       0.      -0.9911   0.       0.\n",
      "    0.       0.       0.       0.       0.       0.       0.       0.\n",
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      "    0.     100.9   ]\n",
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      "    0.       0.       0.       0.       0.       0.       0.       0.\n",
      "    0.0099   1.    ]]\n",
      "--------------------\n",
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      "    0.0099   1.    ]]\n",
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      "    0.0099   1.    ]]\n",
      "--------------------\n",
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      "    0.0099   1.    ]]\n",
      "--------------------\n",
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      "    0.0099   1.    ]]\n",
      "--------------------\n",
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      "    0.0099   1.    ]]\n",
      "--------------------\n",
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      "    0.0099   1.    ]]\n",
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      "    0.0099   1.    ]]\n",
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      "    0.0099   1.    ]]\n",
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      "    0.0099   1.    ]]\n",
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      "    0.0099   1.    ]]\n",
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      "    0.0099   1.    ]]\n",
      "--------------------\n",
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      "    0.0099   1.    ]]\n",
      "--------------------\n",
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      "    0.0099   1.    ]]\n",
      "--------------------\n",
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      "    0.0099   1.    ]]\n",
      "--------------------\n",
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      "    0.0099   1.    ]]\n",
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      "    0.0099 100.9   ]]\n",
      "--------------------\n",
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      "    0.0099 100.9   ]]\n",
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      "    0.0099 100.9   ]]\n",
      "--------------------\n",
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      "    0.0099 100.9   ]]\n",
      "--------------------\n",
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      "    0.0099 100.9   ]]\n",
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      "    0.0099 100.9   ]]\n",
      "--------------------\n",
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      "    0.0099 100.9   ]]\n",
      "--------------------\n",
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      "    0.0099 100.9   ]]\n",
      "--------------------\n",
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      "    0.0099 100.9   ]]\n",
      "--------------------\n",
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      "    0.0099 100.9   ]]\n",
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      "  243.5561 410.1005]]\n",
      "--------------------\n",
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      "  243.5561 410.1005]]\n",
      "--------------------\n",
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      "    0.       0.       0.       0.     218.2005   0.       0.       0.\n",
      "    0.     271.729 ]\n",
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      "    0.       0.       0.       0.       0.       0.       0.       0.\n",
      "  243.5561 410.1005]]\n",
      "--------------------\n",
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      "    0.       0.       0.       0.     218.2005   0.       0.       0.\n",
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      "    0.       0.       0.       0.       0.       0.       0.       0.\n",
      "  243.5561 410.1005]]\n",
      "--------------------\n",
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      "    0.       0.       0.       0.       0.       0.       0.       0.\n",
      "  243.5561 410.1005]]\n",
      "--------------------\n",
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      "    0.       0.       0.       0.       0.      -1.       0.      -1.\n",
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      "    0.       0.      62.7615   0.       0.       0.      -0.9911   0.\n",
      "    0.       0.    ]\n",
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      "    0.       0.       0.       0.     218.2005   0.       0.       0.\n",
      "    0.     271.729 ]\n",
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      "  243.5561 410.1005]]\n"
     ]
    }
   ],
   "source": [
    "# alpha = learning rate\n",
    "alpha = 1\n",
    "# gamma = discount factor\n",
    "gamma = 0.9\n",
    "\n",
    "# Training iterations\n",
    "# s = current state ; a = action ; snext = next state\n",
    "for i in range(100):\n",
    "    s = np.random.randint(0,nbOfStates)        \n",
    "    a = np.random.choice(states[adj_mat[s]==1])\n",
    "    snext = a\n",
    "    Q[s,a]=(1-alpha)*Q[s,a] + (alpha)*(reward_mat[s,a]+gamma*(np.max(Q[snext,:])))\n",
    "    print('-'*20)\n",
    "    print(Q)\n",
    "\n",
    "# Normalize the matrix and remove impossible transitions\n",
    "# print(Q)\n",
    "# Q = Q/np.max(Q)*adj_mat\n",
    "Q = (Q - np.min(Q)) / (np.max(Q) - np.min(Q))\n",
    "Q = Q*adj_mat\n",
    "# print(np.round(Q,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "In room A go to B\n",
      "In room B go to C\n",
      "In room C go to G\n",
      "In room D go to C\n",
      "In room E go to D\n",
      "In room F go to A\n",
      "In room G go to J\n",
      "In room H go to E\n",
      "In room I go to F\n",
      "In room J go to K\n",
      "In room K go to L\n",
      "In room L go to M\n",
      "In room M go to Q\n",
      "In room N go to O\n",
      "In room O go to P\n",
      "In room P go to K\n",
      "In room Q go to EX\n",
      "In room EX go to EX\n"
     ]
    }
   ],
   "source": [
    "# The optimal policy is...\n",
    "sln = np.argmax(Q,axis=1)\n",
    "\n",
    "names_dict = {0:'A', 1:'B', 2:'C', 3:'D', 4:'E', 5:'F', 6:'G', 7:'H',\n",
    "              8:'I', 9:'J', 10:'K', 11:'L', 12:'M', 13:'N', 14:'O', 15:'P',\n",
    "              16:'Q', 17:'EX'}\n",
    "\n",
    "sln_letters = np.vectorize(names_dict.get)(sln)\n",
    "\n",
    "for i in range(nbOfStates):\n",
    "    print('In room '+ names_dict[i]+ ' go to '+sln_letters[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.4248, 0.4731, 0.5268, 0.4731, 0.4248, 0.3813, 0.5864, 0.3813,\n",
       "       0.3422, 0.6527, 0.7263, 0.8081, 0.899 , 0.5268, 0.5864, 0.6527,\n",
       "       1.    , 1.    ])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.max(Q,axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "v_theory = np.array([-1.4, -0.4, +0.6, -0.4, -1.4,\n",
    "                     -2.3,       +1.8,       -2.3, \n",
    "                     -3.0,       +3.1, \n",
    "                                 +4.6, +6.2, +8.0,\n",
    "                     +0.6, +1.8, +3.1,       +10.])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.4, -0.4,  0.6, -0.4, -1.4, -2.3,  1.8, -2.3, -3. ,  3.1,  4.6,\n",
       "        6.2,  8. ,  0.6,  1.8,  3.1, 10. ])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v_theory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.1231, 0.2   , 0.2769, 0.2   , 0.1231, 0.0538, 0.3692, 0.0538,\n",
       "       0.    , 0.4692, 0.5846, 0.7077, 0.8462, 0.2769, 0.3692, 0.4692,\n",
       "       1.    ])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(v_theory - min(v_theory)) / (max(v_theory) - min(v_theory))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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