08_n-armed_Bandit.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exercises and code samples for the course Unsupervised and Reinforcement Learning (AAI-URL) in the Bachelor of AAI at Rosenheim University of Applied Sciences.\n",
    "\n",
    "# n-Armed Bandits\n",
    "\n",
    "This sample introduces the n-armed bandit problem, the conflict between exploration and exploitation, and several ways how to balance this conflict."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Problem defintion:\n",
    "A typical slot machine is a device in which the player pulls a lever arm and receives rewards at some expected rate. Because the expected rate is typically negative, these machines are sometimes referred to as “one-armed bandits”. By analogy, a “multi-armed bandit” is a machine in which there are multiple lever arms to pull, each one of which may pay out at a different expected rate (= reward). \n",
    "\n",
    "The “multi-armed bandit” problem refers to the challenge of constructing a strategy for pulling the levers when one has no prior knowledge of the payout rate for any of the levers. Therefore, one must strike a balance between exploring each of the levers in order to determine their value, while exploiting one’s current knowledge in order to favor high paying levers."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Bandit Class\n",
    "Let's define the bandit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.18  0.57  0.92  1.03 -0.7  -1.    0.21 -0.86  1.2   0.5 ]\n"
     ]
    }
   ],
   "source": [
    "class Bandit:\n",
    "    def __init__(self, k):\n",
    "        # k: number of bandit arms\n",
    "        self.k = k\n",
    "        \n",
    "        # qstar: action values\n",
    "        self.qstar = np.random.normal(size=k).round(2)\n",
    "    \n",
    "    def action(self, a):\n",
    "        return np.random.normal(loc=self.qstar[a])\n",
    "    \n",
    "    def __str__(self):\n",
    "        return np.array_str(self.qstar)\n",
    "\n",
    "print(Bandit(10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The greed action selection algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def greedy_action_selection(k, numsteps):\n",
    "    # k: number of bandit arms\n",
    "    # numsteps: number of steps (repeated action selections)\n",
    "    \n",
    "    # Apossible[t]: list of possible actions at step t\n",
    "    Apossible = {}\n",
    "    \n",
    "    # A[t]: action selected at step t\n",
    "    A = np.zeros((numsteps,))\n",
    "    \n",
    "    # N[a,t]: the number of times action a was selected \n",
    "    #         in steps 0 through t-1\n",
    "    N = np.zeros((k,numsteps+1))\n",
    "    \n",
    "    # R[t]: reward at step t\n",
    "    R = np.zeros((numsteps,))\n",
    "    \n",
    "    # Q[a,t]: estimated value of action a at step t\n",
    "    Q = np.zeros((k,(numsteps+1)))\n",
    "\n",
    "    # Initialize bandit\n",
    "    bandit = Bandit(k)\n",
    "\n",
    "    for t in range(numsteps):\n",
    "\n",
    "        # Select greedy actions as possible actions\n",
    "        Apossible[t] = np.argwhere(Q[:,t] == np.amax(Q[:,t])).flatten()\n",
    "\n",
    "        # Select action randomly from possible actions\n",
    "        a = Apossible[t][np.random.randint(len(Apossible[t]))]\n",
    "\n",
    "        # Record action taken\n",
    "        A[t] = a\n",
    "\n",
    "        # Perform action (= sample reward)\n",
    "        R[t] = bandit.action(a)\n",
    "\n",
    "        # Update action counts\n",
    "        N[:,t+1] = N[:,t]\n",
    "        N[a,t+1] += 1\n",
    "\n",
    "        # Update action value estimates, incrementally\n",
    "        if N[a,t] > 0:\n",
    "            Q[:,t+1] = Q[:,t]\n",
    "            Q[a,t+1] = Q[a,t] + (R[t] - Q[a,t]) / N[a,t]\n",
    "        else:\n",
    "            Q[:,t+1] = Q[:,t]\n",
    "            Q[a,t+1] = R[t]\n",
    "\n",
    "        #Q[:,t] = np.around(Q:t], decimals=2)\n",
    "    return {'bandit': bandit, \n",
    "            'Apossible': Apossible, \n",
    "            'A': A, 'N' : N, 'R' : R, 'Q' : Q}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Single run"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bandit Q: [-1.08 -0.42 -0.04 -0.14  0.49 -0.05 -0.01 -1.   -0.73 -0.26]\n",
      "Action a: [6. 8. 2. 4. 1.]\n",
      "Reward r: [-0.14799025 -1.6830656  -0.98095482 -1.31018117 -2.26459468]\n",
      "Est    Q:\n",
      "[[ 0.          0.          0.          0.          0.          0.        ]\n",
      " [ 0.          0.          0.          0.          0.         -2.26459468]\n",
      " [ 0.          0.          0.         -0.98095482 -0.98095482 -0.98095482]\n",
      " [ 0.          0.          0.          0.          0.          0.        ]\n",
      " [ 0.          0.          0.          0.         -1.31018117 -1.31018117]\n",
      " [ 0.          0.          0.          0.          0.          0.        ]\n",
      " [ 0.         -0.14799025 -0.14799025 -0.14799025 -0.14799025 -0.14799025]\n",
      " [ 0.          0.          0.          0.          0.          0.        ]\n",
      " [ 0.          0.         -1.6830656  -1.6830656  -1.6830656  -1.6830656 ]\n",
      " [ 0.          0.          0.          0.          0.          0.        ]]\n"
     ]
    }
   ],
   "source": [
    "k = 10\n",
    "numsteps = 5\n",
    "\n",
    "bandit_task = greedy_action_selection(k, numsteps)\n",
    "\n",
    "print('Bandit Q: %s' % bandit_task['bandit'])\n",
    "print('Action a: %s' % bandit_task['A'])\n",
    "print('Reward r: %s' % bandit_task['R'])\n",
    "print('Est    Q:')\n",
    "print('%s' %bandit_task['Q'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conversation over 500 plays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k = 10\n",
    "numsteps = 500\n",
    "numtasks = 2000\n",
    "\n",
    "avgR = np.zeros((numsteps, ))\n",
    "for task in range(numtasks):\n",
    "    bandit_task = greedy_action_selection(k,numsteps)\n",
    "    avgR += bandit_task['R']\n",
    "avgR /= numtasks\n",
    "\n",
    "plt.plot(avgR) ;\n",
    "plt.ylabel('Average reward') ;\n",
    "plt.xlabel('Steps (number of plays)') ;\n",
    "plt.xlim(-5) ;"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}