abhsharma.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "2RM-jwrRDFw9"
   },
   "source": [
    "# Multi-armed bandits (MAB) implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "_l9AhBsJDFw-"
   },
   "outputs": [],
   "source": [
    "# Do not edit. These are the only imports permitted.\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "from numpy.linalg import inv\n",
    "import matplotlib.pyplot as plt\n",
    "from abc import ABC, abstractmethod"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "fMCitxQtDFxC"
   },
   "source": [
    "## 1. Implementing ε-Greedy and UCB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "9WtlOOYhDFxC"
   },
   "outputs": [],
   "source": [
    "class MAB(ABC):\n",
    "    \"\"\"\n",
    "    Abstract class that represents a multi-armed bandit (MAB)\n",
    "    \"\"\"\n",
    "    \n",
    "    @abstractmethod\n",
    "    def play(self, tround, context):\n",
    "        \"\"\"\n",
    "        Play a round\n",
    "        \n",
    "        Arguments\n",
    "        =========\n",
    "        tround : int\n",
    "            positive integer identifying the round\n",
    "        \n",
    "        context : 1D float array, shape (self.ndims * self.narms), optional\n",
    "            context given to the arms\n",
    "        \n",
    "        Returns\n",
    "        =======\n",
    "        arm : int\n",
    "            the positive integer arm id for this round\n",
    "        \"\"\"\n",
    "    \n",
    "    @abstractmethod\n",
    "    def update(self, arm, reward, context):\n",
    "        \"\"\"\n",
    "        Updates the internal state of the MAB after a play\n",
    "        \n",
    "        Arguments\n",
    "        =========\n",
    "        arm : int\n",
    "            a positive integer arm id in {1, ..., self.narms}\n",
    "        \n",
    "        reward : float\n",
    "            reward received from arm\n",
    "        \n",
    "        context : 1D float array, shape (self.ndims * self.narms), optional\n",
    "            context given to arms\n",
    "        \"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "QwGoY29VDFxG"
   },
   "outputs": [],
   "source": [
    "class EpsGreedy(MAB):\n",
    "    \"\"\"\n",
    "    Epsilon-Greedy multi-armed bandit\n",
    "\n",
    "    Arguments\n",
    "    =========\n",
    "    narms : int\n",
    "        number of arms\n",
    "\n",
    "    epsilon : float\n",
    "        explore probability\n",
    "\n",
    "    Q0 : float, optional\n",
    "        initial value for the arms\n",
    "    \"\"\"\n",
    "    \n",
    "    def __init__(self, narms, epsilon, Q0=np.inf):\n",
    "      \n",
    "        # basic input checks\n",
    "        assert type(narms) is int, 'input type int required for narms'\n",
    "        assert type(epsilon) is float, 'input type float required for epsilon'\n",
    "        assert type(Q0) is float, 'input type float required for epsilon'\n",
    "        assert narms > 0, \"number of arms should be greater than 0\"\n",
    "        assert 0 <= epsilon <= 1, \"epsilon should be in [0,1] range\"\n",
    "        \n",
    "        # initilize MAB parameters\n",
    "        self.narms = narms\n",
    "        self.epsilon = epsilon\n",
    "        self.Q0 = Q0\n",
    "        \n",
    "        # initilize MAB state\n",
    "        self.arm_selection = np.zeros(narms)\n",
    "        self.arm_rewards_collected = np.zeros(narms)\n",
    "        \n",
    "    def play(self, tround, context=None):\n",
    "        # exploitation vs exploration\n",
    "        \n",
    "        # setting seed to reproduce results reliably\n",
    "        np.random.seed(10007)\n",
    "        if np.random.random() > self.epsilon:\n",
    "            \n",
    "            # exploit arm\n",
    "            bounds = [0] * self.narms\n",
    "            \n",
    "            for arm in range(0,self.narms):\n",
    "              \n",
    "                # check if arm is selected once or not\n",
    "                if self.arm_selection[arm] == 0:\n",
    "                  \n",
    "                    # arm is still not selected - set average reward to Q0\n",
    "                    bounds[arm] = self.Q0\n",
    "                else:\n",
    "                  \n",
    "                    # arm is selected at least once\n",
    "                    arm_reward = self.arm_rewards_collected[arm]\n",
    "                    arm_selection = self.arm_selection[arm]\n",
    "                    \n",
    "                    # calculate current average reward for the arm\n",
    "                    bounds[arm] = arm_reward/arm_selection\n",
    "                    \n",
    "            # getting maximum average reward providing arm\n",
    "            maximum_bound = np.max(bounds)\n",
    "            \n",
    "            # handling tie-breaking using uniformly-at-random selection\n",
    "            # setting seed to reproduce results reliably\n",
    "            np.random.seed(10007)\n",
    "            arm_to_play = np.random.choice(np.where(bounds==maximum_bound)[0],1)[0]\n",
    "            \n",
    "            # returning an arm integer in {1,...,self.narms}\n",
    "            return arm_to_play+1\n",
    "        else:\n",
    "            # explore arms\n",
    "            \n",
    "            # randomly picking arm from 0-9\n",
    "            # setting seed to reproduce results reliably\n",
    "            np.random.seed(10007)\n",
    "            arm_to_play = np.random.randint(self.narms-1)\n",
    "            \n",
    "            # returning an arm integer in {1,...,self.narms}\n",
    "            return arm_to_play+1\n",
    "        \n",
    "    def update(self, arm, reward, context=None):\n",
    "        # update played arm\n",
    "        \n",
    "        # verifying arm input\n",
    "        assert arm <= self.narms, \"arm is larger than property narms\"\n",
    "        \n",
    "        # Get arm index\n",
    "        arm_idx = arm-1\n",
    "        \n",
    "        # update state of played arm\n",
    "        self.arm_selection[arm_idx] = self.arm_selection[arm_idx] + 1\n",
    "        self.arm_rewards_collected[arm_idx] = self.arm_rewards_collected[arm_idx] + reward"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "xJ8MLdDdDFxJ"
   },
   "outputs": [],
   "source": [
    "class UCB(MAB):\n",
    "    \"\"\"\n",
    "    Upper Confidence Bound (UCB) multi-armed bandit\n",
    "\n",
    "    Arguments\n",
    "    =========\n",
    "    narms : int\n",
    "        number of arms\n",
    "\n",
    "    rho : float\n",
    "        positive real explore-exploit parameter\n",
    "\n",
    "    Q0 : float, optional\n",
    "        initial value for the arms\n",
    "    \"\"\"\n",
    "    \n",
    "    def __init__(self, narms, rho, Q0=np.inf):\n",
    "      \n",
    "        # basic input checks\n",
    "        assert type(narms) is int, 'input type int required for narms'\n",
    "        assert type(rho) is float, 'input type float required for rho'\n",
    "        assert type(Q0) is float, 'input type float required for epsilon'\n",
    "        assert narms > 0, \"number of arms should be greater than 0\"\n",
    "        assert rho > 0, \"rho should be greater than 0\"\n",
    "      \n",
    "        # initilize MAB parameters\n",
    "        self.narms = narms\n",
    "        self.rho = rho\n",
    "        self.Q0 = Q0\n",
    "        \n",
    "        # initilize MAB state\n",
    "        self.arm_selection = np.zeros(narms)\n",
    "        self.arm_rewards_collected = np.zeros(narms)\n",
    "\n",
    "    def play(self, tround, context=None):\n",
    "        # initilize play parameter\n",
    "        bounds = [0] * self.narms\n",
    "        \n",
    "        # verify tround parameter\n",
    "        assert tround > 0, \"tround should be greater than 0\"\n",
    "        \n",
    "        # calculate upper bounds for each arm\n",
    "        for arm in range(0,self.narms):\n",
    "          \n",
    "            # check if arm is selected once or not\n",
    "            if self.arm_selection[arm] == 0:\n",
    "              \n",
    "                # arm is still not selected - set average reward to Q0\n",
    "                bounds[arm] = self.Q0\n",
    "            else:\n",
    "              \n",
    "                # arm is selected at least once\n",
    "                arm_reward = self.arm_rewards_collected[arm]\n",
    "                arm_selection = self.arm_selection[arm]\n",
    "                \n",
    "                # calculate Upper Confidence Bound(UCB) for the arm\n",
    "                average_reward = arm_reward/arm_selection\n",
    "                delta = np.sqrt(self.rho*(np.log(tround)/arm_selection))\n",
    "                bounds[arm] = average_reward + delta\n",
    "\n",
    "        # getting maximum Upper Confidence Bound(UCB) providing arm\n",
    "        maximum_bound = np.max(bounds)\n",
    "            \n",
    "        # handling tie-breaking using uniformly-at-random selection\n",
    "        # setting seed to reproduce results reliably\n",
    "        np.random.seed(20003)\n",
    "        arm_to_play = np.random.choice(np.where(bounds==maximum_bound)[0],1)[0]\n",
    "            \n",
    "        # returning an arm integer in {1,...,self.narms}\n",
    "        return arm_to_play+1\n",
    "        \n",
    "    def update(self, arm, reward, context=None):\n",
    "        # update played arm\n",
    "        \n",
    "        # verifying arm input\n",
    "        assert arm <= self.narms, \"arm is larger than property narms\"\n",
    "        \n",
    "        # Getting arm index\n",
    "        arm_idx = arm-1\n",
    "        \n",
    "        # update state of played arm\n",
    "        self.arm_selection[arm_idx] = self.arm_selection[arm_idx] + 1\n",
    "        self.arm_rewards_collected[arm_idx] = self.arm_rewards_collected[arm_idx] + reward"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "QyMzEy4dDFxM"
   },
   "source": [
    "## 2. The Basic Thompson Bandit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "51EzB_cYDFxN"
   },
   "outputs": [],
   "source": [
    "class BetaThompson(MAB):\n",
    "    \"\"\"\n",
    "    Beta-Bernoulli Thompson sampling multi-armed bandit\n",
    "\n",
    "    Arguments\n",
    "    =========\n",
    "    narms : int\n",
    "        number of arms\n",
    "\n",
    "    alpha0 : float, optional\n",
    "        positive real prior hyperparameter\n",
    "\n",
    "    beta0 : float, optional\n",
    "        positive real prior hyperparameter\n",
    "    \"\"\"\n",
    "    \n",
    "    def __init__(self, narms, alpha0=1.0, beta0=1.0):\n",
    "      \n",
    "        # basic input checks\n",
    "        assert type(narms) is int, 'input type int required for narms'\n",
    "        assert type(alpha0) is float, 'input type float required for alpha0'\n",
    "        assert type(beta0) is float, 'input type float required for beta0'\n",
    "        assert narms > 0, \"number of arms should be greater than 0\"\n",
    "        assert alpha0 > 0, \"alpha0 should be greater than 0\"\n",
    "        assert beta0 > 0, \"alpha0 should be greater than 0\"\n",
    "        \n",
    "        # initilize MAB parameters\n",
    "        self.narms = narms\n",
    "        self.alpha0 = alpha0\n",
    "        self.beta0 = beta0\n",
    "        \n",
    "        # initilize MAB state\n",
    "        self.observed_successes = [0] * narms\n",
    "        self.observed_failures = [0] * narms\n",
    "    \n",
    "    def play(self, tround, context=None):\n",
    "        # initilize play parameters\n",
    "        samples = [0] * self.narms\n",
    "        \n",
    "        for arm in range(0,self.narms):\n",
    "            # get observed success for the arm\n",
    "            S_i = self.observed_successes[arm]\n",
    "            \n",
    "            # get observed failure for the arm\n",
    "            F_i = self.observed_failures[arm]\n",
    "            \n",
    "            # generate sample from beta distribution\n",
    "            # setting seed to reproduce results reliably\n",
    "            np.random.seed(30005)\n",
    "            samples[arm] = np.random.beta(S_i + self.alpha0, F_i + self.beta0)\n",
    "\n",
    "        # get value-maximising arm from generated samples\n",
    "        maximum_sample_value = np.max(samples)\n",
    "            \n",
    "        # handle tie-breaking using uniformly-at-random selection\n",
    "        # setting seed to reproduce results reliably\n",
    "        np.random.seed(30005)\n",
    "        arm_to_play = np.random.choice(np.where(samples==maximum_sample_value)[0],1)[0]\n",
    "            \n",
    "        # returning an arm integer in {1,...,self.narms}\n",
    "        return arm_to_play+1\n",
    "        \n",
    "    def update(self, arm, reward, context=None):\n",
    "        # update played arm\n",
    "        \n",
    "        # verifying arm input\n",
    "        assert arm <= self.narms, \"arm is larger than property narms\"\n",
    "        \n",
    "        # Getting arm index\n",
    "        arm_idx = arm-1\n",
    "        \n",
    "        # checking reward\n",
    "        if reward==1:\n",
    "            # update success if reward is observed\n",
    "            self.observed_successes[arm_idx] = self.observed_successes[arm_idx] + 1\n",
    "        else:\n",
    "            # update failure if reward is not observed\n",
    "            self.observed_failures[arm_idx] = self.observed_failures[arm_idx] + 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "XM7k3BicDFxQ"
   },
   "source": [
    "## 3. Off-Policy Evaluation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "vdN0VFigDFxQ"
   },
   "outputs": [],
   "source": [
    "def offlineEvaluate(mab, arms, rewards, contexts, nrounds=None):\n",
    "    \"\"\"\n",
    "    Offline evaluation of a multi-armed bandit\n",
    "    \n",
    "    Arguments\n",
    "    =========\n",
    "    mab : instance of MAB\n",
    "    \n",
    "    arms : 1D int array, shape (nevents,) \n",
    "        integer arm id for each event\n",
    "    \n",
    "    rewards : 1D float array, shape (nevents,)\n",
    "        reward received for each event\n",
    "    \n",
    "    contexts : 2D float array, shape (nevents, mab.narms*nfeatures)\n",
    "        contexts presented to the arms (stacked horizontally) \n",
    "        for each event.\n",
    "        \n",
    "    nrounds : int, optional\n",
    "        number of matching events to evaluate `mab` on.\n",
    "    \n",
    "    Returns\n",
    "    =======\n",
    "    out : 1D float array\n",
    "        rewards for the matching events\n",
    "    \"\"\"\n",
    "    \n",
    "    # basic input checks to ensure everything works after assertions are passed\n",
    "    assert isinstance(mab,MAB), 'MAB instance required'\n",
    "    assert type(arms) is np.ndarray, 'arms should be numpy array'\n",
    "    assert type(rewards) is np.ndarray, 'rewards should be numpy array'\n",
    "    assert type(contexts) is np.ndarray, 'contexts should be numpy array'\n",
    "    if nrounds is not None:\n",
    "        assert type(nrounds) is int, 'input type int required for nrounds'\n",
    "        assert nrounds > 0, 'nrounds should be greater than 0'\n",
    "    assert 'int' in str(arms.dtype), 'arms should be int numpy array'\n",
    "    assert 'float' in str(rewards.dtype), 'rewards should be float numpy array'\n",
    "    assert 'float' in str(contexts.dtype), 'contexts should be float numpy array'\n",
    "    assert arms.ndim == 1, 'arms should be 1D numpy array (nevents,) '\n",
    "    assert rewards.ndim == 1, 'rewards should be 1D numpy array (nevents,)'\n",
    "    assert contexts.ndim == 2, 'contexts should be 2D numpy array (nevents, mab.narms*nfeatures)'\n",
    "\n",
    "    # initially empty history\n",
    "    history = []\n",
    "    \n",
    "    # initially empty payoff\n",
    "    out = []\n",
    "    \n",
    "    # get total number of events\n",
    "    T = arms.shape[0]\n",
    "    \n",
    "    # ensuring there are events to evaluate\n",
    "    assert T > 0, \"There are no events for offline evaluation\"\n",
    "    \n",
    "    # initilize control parameters\n",
    "    events_parsed = 0\n",
    "    all_events_parsed = False\n",
    "    \n",
    "    # sequentially parse stream of events\n",
    "    for t in range(0,T):\n",
    "        \n",
    "        # repeat until matching arm is found\n",
    "        while(True):\n",
    "            \n",
    "            # if all events are parsed - stop processing\n",
    "            if events_parsed == T:\n",
    "                all_events_parsed = True\n",
    "                break\n",
    "            \n",
    "            # Get next event    \n",
    "            # get selected arm\n",
    "            a = arms[events_parsed]\n",
    "            # get observed payoff for the arm\n",
    "            r_a = rewards[events_parsed]\n",
    "            # get observed context for the arm\n",
    "            context = contexts[events_parsed,:]\n",
    "            \n",
    "            # keeping track of parsed events\n",
    "            events_parsed += 1\n",
    "     \n",
    "            # set required round on the basis of history recorded\n",
    "            tround = len(history)+1\n",
    "            # play arm for tround\n",
    "            arm = mab.play(tround,context)\n",
    "            \n",
    "            # check if arm is matched or not\n",
    "            if arm == a:\n",
    "                # matching arm found - update played arm\n",
    "                mab.update(arm,r_a,context)\n",
    "                break \n",
    "        \n",
    "        # check if all events are parsed       \n",
    "        if all_events_parsed:\n",
    "            # stop processing\n",
    "            break\n",
    "            \n",
    "        # record event tuple in history for each matched round\n",
    "        event = (tround,a,r_a,context)\n",
    "        history.append(event)      \n",
    "        \n",
    "        # add observed payoff for the matched arm\n",
    "        out.append(r_a)\n",
    "        \n",
    "        # check if required rounds are reached, if provided\n",
    "        if nrounds is not None and len(history) == nrounds:\n",
    "            break\n",
    "    \n",
    "    # return per round rewards recorded\n",
    "    return out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "_76guiFIO8Tb"
   },
   "outputs": [],
   "source": [
    "# loading dataset\n",
    "dataset = np.loadtxt(\"dataset.txt\")\n",
    "\n",
    "# get arms from dataset\n",
    "arms = dataset[:,0].astype('int')\n",
    "# get rewards from dataset\n",
    "rewards = dataset[:,1].astype('float')\n",
    "# get contexts from dataset \n",
    "contexts = dataset[:,2:].astype('float')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 35
    },
    "colab_type": "code",
    "id": "6_j1MmxSDFxT",
    "outputId": "ad4c02ab-3705-451c-fe4e-d9530a9656b7"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "EpsGreedy average reward 0.145\n"
     ]
    }
   ],
   "source": [
    "mab = EpsGreedy(10, 0.05)\n",
    "results_EpsGreedy = offlineEvaluate(mab, arms, rewards, contexts, 800)\n",
    "print('EpsGreedy average reward', np.mean(results_EpsGreedy))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 35
    },
    "colab_type": "code",
    "id": "KJk_Hh_pDFxX",
    "outputId": "a18a24fc-fbd4-4122-c9f9-e38a5fe18ffc"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "UCB average reward 0.165\n"
     ]
    }
   ],
   "source": [
    "mab = UCB(10, 1.0)\n",
    "results_UCB = offlineEvaluate(mab, arms, rewards, contexts, 800)\n",
    "print('UCB average reward', np.mean(results_UCB))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 35
    },
    "colab_type": "code",
    "id": "q5zqfGldDFxa",
    "outputId": "2ec8ba68-6743-4209-8f7e-decada1b99fe"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "BetaThompson average reward 0.255\n"
     ]
    }
   ],
   "source": [
    "mab = BetaThompson(10, 1.0, 1.0)\n",
    "results_BetaThompson = offlineEvaluate(mab, arms, rewards, contexts, 800)\n",
    "print('BetaThompson average reward', np.mean(results_BetaThompson))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ARytP_8eDFxc"
   },
   "source": [
    "## 4. Contextual Bandits - LinUCB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "33en3eoHDFxd"
   },
   "outputs": [],
   "source": [
    "class LinUCB(MAB):\n",
    "    \"\"\"\n",
    "    Contextual multi-armed bandit (LinUCB)\n",
    "\n",
    "    Arguments\n",
    "    =========\n",
    "    narms : int\n",
    "        number of arms\n",
    "\n",
    "    ndims : int\n",
    "        number of dimensions for each arm's context\n",
    "\n",
    "    alpha : float\n",
    "        positive real explore-exploit parameter\n",
    "    \"\"\"\n",
    "    \n",
    "    def __init__(self, narms, ndims, alpha):\n",
    "      \n",
    "        # basic input checks\n",
    "        assert type(narms) is int, 'input type int required for narms'\n",
    "        assert type(ndims) is int, 'input type int required for ndims'\n",
    "        assert type(alpha) is float, 'input type float required for alpha'\n",
    "        assert narms > 0, \"number of arms should be greater than 0\"\n",
    "        assert ndims > 0, \"ndims should be greater than 0\"\n",
    "        assert alpha > 0, \"alpha should be greater than 0\"\n",
    "        \n",
    "        # initilize MAB parameters\n",
    "        self.narms = narms\n",
    "        self.ndims = ndims\n",
    "        self.alpha = alpha\n",
    "        \n",
    "        # initilize MAB state\n",
    "        self.A_arm_param = [None] * narms\n",
    "        self.b_arm_param = [None] * narms\n",
    "        \n",
    "    def play(self, tround, context):\n",
    "        # initilize play parameters\n",
    "        bounds = [0] * self.narms\n",
    "      \n",
    "        # perform operation for all arms\n",
    "        for arm in range(0,self.narms):\n",
    "            \n",
    "            # observe features for arm in loop\n",
    "            arm_features = np.expand_dims(np.transpose(context[(arm*10):(arm*10)+10]),axis=1)\n",
    "            \n",
    "            # check if arm is new or not\n",
    "            if self.A_arm_param[arm] is None:\n",
    "              \n",
    "                # arm is new - perform initilization of A matrix and b vector for arm\n",
    "                self.A_arm_param[arm] = np.identity(self.ndims)\n",
    "                self.b_arm_param[arm] = np.zeros((self.ndims,1))\n",
    "            \n",
    "            # calculate estimate of the coefficients (theta) for the arm\n",
    "            A_arm = self.A_arm_param[arm]\n",
    "            b_arm = self.b_arm_param[arm]\n",
    "            A_arm_inv = inv(A_arm)\n",
    "            theta_hat_arm = np.dot(inv(A_arm),b_arm)\n",
    "            \n",
    "            # calculate upper confidence interval for the arm using tight UCB \n",
    "            delta = self.alpha * np.sqrt(np.dot(np.dot(np.transpose(arm_features),A_arm_inv),arm_features))\n",
    "            bounds[arm] = np.dot(np.transpose(theta_hat_arm),arm_features) + delta\n",
    "       \n",
    "        # getting maximum Upper Confidence Bound(UCB) providing arm\n",
    "        maximum_bound = np.max(bounds)\n",
    "            \n",
    "        # handling tie-breaking using uniformly-at-random selection\n",
    "        # setting seed to reproduce results reliably\n",
    "        np.random.seed(40001)\n",
    "        arm_to_play = np.random.choice(np.where(bounds==maximum_bound)[0],1)[0]\n",
    "            \n",
    "        # returning an arm integer in {1,...,self.narms}\n",
    "        return arm_to_play+1\n",
    "    \n",
    "    def update(self, arm, reward, context):\n",
    "        # update played arm\n",
    "        \n",
    "        # verifying arm input\n",
    "        assert arm <= self.narms, \"arm is larger than property narms\"\n",
    "        \n",
    "        # Getting arm index\n",
    "        arm_idx = arm-1\n",
    "        \n",
    "        # observe features for the played arm\n",
    "        arm_features = np.expand_dims(np.transpose(context[(arm_idx*10):(arm_idx*10)+10]),axis=1)\n",
    "        \n",
    "        # update state of played arm\n",
    "        self.A_arm_param[arm_idx] = self.A_arm_param[arm_idx] + np.dot(arm_features,np.transpose(arm_features))\n",
    "        self.b_arm_param[arm_idx] = self.b_arm_param[arm_idx] + reward*arm_features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 35
    },
    "colab_type": "code",
    "id": "WLUI8aaEDFxg",
    "outputId": "27a0b437-95c2-4a98-afc8-8116550c7cba"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LinUCB average reward 0.53\n"
     ]
    }
   ],
   "source": [
    "mab = LinUCB(10, 10, 1.0)\n",
    "results_LinUCB = offlineEvaluate(mab, arms, rewards, contexts, 800)\n",
    "print('LinUCB average reward', np.mean(results_LinUCB))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "PhQkpQQ0DFxi"
   },
   "source": [
    "## 5. Contextual Bandits - LinThompson"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "bHPEr77bDFxj"
   },
   "outputs": [],
   "source": [
    "class LinThompson(MAB):\n",
    "    \"\"\"\n",
    "    Contextual Thompson sampled multi-armed bandit (LinThompson)\n",
    "\n",
    "    Arguments\n",
    "    =========\n",
    "    narms : int\n",
    "        number of arms\n",
    "\n",
    "    ndims : int\n",
    "        number of dimensions for each arm's context\n",
    "\n",
    "    v : float\n",
    "        positive real explore-exploit parameter\n",
    "    \"\"\"\n",
    "    \n",
    "    def __init__(self, narms, ndims, v):\n",
    "      \n",
    "        # basic input checks\n",
    "        assert type(narms) is int, 'input type int required for narms'\n",
    "        assert type(ndims) is int, 'input type int required for ndims'\n",
    "        assert type(v) is float, 'input type float required for v'\n",
    "        assert narms > 0, \"number of arms should be greater than 0\"\n",
    "        assert ndims > 0, \"ndims should be greater than 0\"\n",
    "        assert v > 0, \"v should be greater than 0\"\n",
    "        \n",
    "        # initilize MAB parameters\n",
    "        self.narms = narms\n",
    "        self.ndims = ndims\n",
    "        self.v = v\n",
    "        \n",
    "        # initilize MAB state\n",
    "        self.B = np.identity(ndims)        # ndims x ndims\n",
    "        self.mu_hat = np.zeros((ndims,1))  # ndims x 1\n",
    "        self.f = np.zeros((ndims,1))       # ndims x 1\n",
    "        \n",
    "    def play(self, tround, context):\n",
    "        # initilize play parameters\n",
    "        bounds = [0] * self.narms\n",
    "        \n",
    "        # generate samples from multivariate normal distribution \n",
    "        mean = np.transpose(self.mu_hat)[0]\n",
    "        covariance_matrix = ((self.v)**2)*np.linalg.inv(self.B)\n",
    "        # setting seed to reproduce results reliably\n",
    "        np.random.seed(50005) # [bug] seed sometimes unreliable for multivariate normal\n",
    "        samples = np.random.multivariate_normal(mean, covariance_matrix)\n",
    "        # (ndims x 1) samples\n",
    "        sample_mu_tilde = np.expand_dims(samples,axis=1)\n",
    "        \n",
    "        # perform operation for all arms\n",
    "        for arm in range(0,self.narms):\n",
    "            \n",
    "            # get context for the arm (ndims x 1)\n",
    "            arm_context = np.expand_dims(np.transpose(context[(arm*10):(arm*10)+10]),axis=1)\n",
    "            \n",
    "            # calculate value for the arm\n",
    "            bounds[arm] = np.dot(np.transpose(arm_context),sample_mu_tilde)\n",
    "            \n",
    "        # get value-maximising arm from generated bounds\n",
    "        maximum_arm_value = np.max(bounds)\n",
    "            \n",
    "        # handle tie-breaking using uniformly-at-random selection\n",
    "        # setting seed to reproduce results reliably\n",
    "        np.random.seed(50005)\n",
    "        arm_to_play = np.random.choice(np.where(bounds==maximum_arm_value)[0],1)[0]\n",
    "            \n",
    "        # returning an arm integer in {1,...,self.narms}\n",
    "        return arm_to_play+1\n",
    "    \n",
    "    def update(self, arm, reward, context):\n",
    "        # update played arm\n",
    "        \n",
    "        # verifying arm input\n",
    "        assert arm <= self.narms, \"arm is larger than property narms\"\n",
    "        \n",
    "        # Getting arm index\n",
    "        arm_idx = arm-1\n",
    "        \n",
    "        # get context for the played arm\n",
    "        arm_context = np.expand_dims(np.transpose(context[(arm_idx*10):(arm_idx*10)+10]),axis=1)\n",
    "        \n",
    "        # update state of the played arm\n",
    "        self.B = self.B + np.dot(arm_context,np.transpose(arm_context))\n",
    "        self.f = self.f + arm_context*reward\n",
    "        self.mu_hat = np.dot(inv(self.B),self.f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 35
    },
    "colab_type": "code",
    "id": "yezaM_09DFxp",
    "outputId": "82e9e44a-3542-409c-94f0-887b96d8f5db"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LinThompson average reward 0.35625\n"
     ]
    }
   ],
   "source": [
    "mab = LinThompson(10, 10, 1.0)\n",
    "results_LinThompson = offlineEvaluate(mab, arms, rewards, contexts, 800)\n",
    "print('LinThompson average reward', np.mean(results_LinThompson))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "xawY_20CDFxr"
   },
   "source": [
    "## 6. Evaluation\n",
    "### 6.A."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 488
    },
    "colab_type": "code",
    "id": "nbQK9D5XDFxs",
    "outputId": "3d622bb2-17fc-4cbd-a95f-1a8803681f3a"
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 768x512 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# setting figure parameters\n",
    "FIGURE_RESOLUTION = 128\n",
    "plt.rcParams['figure.dpi'] = FIGURE_RESOLUTION\n",
    "\n",
    "# Evaluation function for plot\n",
    "\n",
    "def evaluation(T, params):\n",
    "    # initilize evaluation parameters\n",
    "    eps_greedy_cumulative = [0] * T\n",
    "    ucb_cumulative = [0] * T\n",
    "    beta_thompson_cumulative = [0] * T\n",
    "    linUCB_cumulative = [0] * T\n",
    "    linThompson_cumulative = [0] * T\n",
    "    \n",
    "    # Run offline evaluation for algorithms\n",
    "    # EpsilonGreedy\n",
    "    mab = EpsGreedy(10, params['eps_greedy'])\n",
    "    results_EpsGreedy = offlineEvaluate(mab, arms, rewards, contexts, T)\n",
    "    # UCB\n",
    "    mab = UCB(10, params['ucb'])\n",
    "    results_UCB = offlineEvaluate(mab, arms, rewards, contexts, T)\n",
    "    # BetaThompson\n",
    "    mab = BetaThompson(10, params['beta_thompson'][0], params['beta_thompson'][1])\n",
    "    results_BetaThompson = offlineEvaluate(mab, arms, rewards, contexts, T)\n",
    "    # LinUCB\n",
    "    mab = LinUCB(10, 10, params['lin_ucb'])\n",
    "    results_LinUCB = offlineEvaluate(mab, arms, rewards, contexts, T)\n",
    "    # LinThompson\n",
    "    mab = LinThompson(10, 10, params['lin_thompson'])\n",
    "    results_LinThompson = offlineEvaluate(mab, arms, rewards, contexts, T)\n",
    "\n",
    "    # Get cumulative reward per round\n",
    "    for t in range(1,T):\n",
    "        eps_greedy_cumulative[t] = eps_greedy_cumulative[t-1] + results_EpsGreedy[t-1]\n",
    "        ucb_cumulative[t] = ucb_cumulative[t-1] + results_UCB[t-1]\n",
    "        beta_thompson_cumulative[t] = beta_thompson_cumulative[t-1] + results_BetaThompson[t-1]\n",
    "        linUCB_cumulative[t] = linUCB_cumulative[t-1] + results_LinUCB[t-1]\n",
    "        linThompson_cumulative[t] = linThompson_cumulative[t-1] + results_LinThompson[t-1]\n",
    "\n",
    "    # plot cumulative reward for algorithms\n",
    "    t = np.arange(T)\n",
    "    plt.plot(t, eps_greedy_cumulative)\n",
    "    plt.plot(t, ucb_cumulative)\n",
    "    plt.plot(t, beta_thompson_cumulative)\n",
    "    plt.plot(t, linUCB_cumulative)\n",
    "    plt.plot(t, linThompson_cumulative)\n",
    "    plt.legend(['EPSGreedy', 'UCB', 'BetaThompson', 'LinUCB', 'LinThompson'], loc='upper left')\n",
    "    plt.xlabel('Rounds')\n",
    "    plt.ylabel('Cumulative Reward')\n",
    "    plt.show()\n",
    "    \n",
    "# Evaluating algorithms for 800 rounds with provided hyperparameters\n",
    "evaluation(T=800,params={'eps_greedy':0.05, 'ucb':1.0, 'beta_thompson':[1.0,1.0], 'lin_ucb':1.0, 'lin_thompson':1.0})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Qig1dY0nDFxv"
   },
   "source": [
    "### 6.B."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Le4XqqasoT6t"
   },
   "source": [
    "In order to optimise hyperparameters, `GridSearchMAB` class is implemented which can take any of the above `MAB` based classes with 1 hyperparameter. So, this class will not support `BetaThompson` directly, but it can be enhanced easily.\n",
    "\n",
    "`GridSearchMAB` is included with `strategy` parameter which can be used to include any grid-search strategy that is compatible with our MAB classes. Currently, it is implemented with basic naive grid-search strategy to find the most optimised hyperparameter:\n",
    "\n",
    "- `Naive strategy`: In this strategy, `GridSearchMAB` will initilize `MAB` class with provided grid parameters which includes a range for target hyperparameter. We can then evaluate parameters provided in the range sequentially on the scoring function by keeping track of the results and corresponding mean score. Finally, we can get the best parameter from the range based on the maximum mean score.\n",
    "\n",
    "This strategy is implemented in the class below, followed by results of LinUCB and LinThompson."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "ZmAY6Y1WUHXL"
   },
   "outputs": [],
   "source": [
    "class GridSearchMAB:\n",
    "  \n",
    "    def __init__(self, mab, param_grid, scoring, strategy='naive', verbose=0):\n",
    "        # initilize gridsearch parameters\n",
    "        self.mab = mab\n",
    "        self.param_grid = param_grid\n",
    "        self.scoring = scoring\n",
    "        self.verbose = verbose\n",
    "        self.strategy = strategy\n",
    "        \n",
    "        # initilize gridsearch state\n",
    "        self.results_ = {'mean_score':[],'evaluate_results':[],'params':[]}\n",
    "        self.best_param_ = None\n",
    "        self.best_score_ = None\n",
    "      \n",
    "    def fit(self,arms,rewards,contexts=None):\n",
    "        # fit data on the basis of provided strategy\n",
    "        if self.strategy == 'naive':\n",
    "            self.naive_strategy(arms,rewards,contexts)\n",
    "           \n",
    "    def naive_strategy(self,arms,rewards,contexts=None):\n",
    "        # get provided parameters\n",
    "        prange = self.param_grid['param_range']\n",
    "        narms = self.param_grid['narms']\n",
    "        ndims = self.param_grid['ndims']\n",
    "        rounds = self.param_grid['rounds']\n",
    "        for param in prange:\n",
    "            \n",
    "            # making it compatible with other MABs (except BetaThompson)\n",
    "            if ndims is not None:\n",
    "                mabobj = self.mab(narms,ndims,float(param))\n",
    "            else:\n",
    "                mabobj = self.mab(narms,float(param))\n",
    "            \n",
    "            # evaluate mab on provided scoring function\n",
    "            result = self.scoring(mabobj, arms, rewards, contexts, rounds)\n",
    "            \n",
    "            # store results in state\n",
    "            self.results_['params'].append(param)\n",
    "            self.results_['evaluate_results'].append(result)\n",
    "            mean_score = np.mean(result)\n",
    "            self.results_['mean_score'].append(mean_score)\n",
    "            \n",
    "            # message printing if required\n",
    "            if self.verbose == 1:\n",
    "              print('param: '+str(param)+' mean_score: '+str(mean_score))\n",
    "        \n",
    "        # get best parameter and score\n",
    "        np_score = np.array(self.results_['mean_score'])\n",
    "        self.best_score_ = np.max(np_score)\n",
    "        self.best_param_ = float(prange[np.argmax(np_score)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 397
    },
    "colab_type": "code",
    "id": "dAYX1oYtbRee",
    "outputId": "d391a9be-4247-43ee-f292-2af7afac4da8"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "param: 1e-05 mean_score: 0.64625\n",
      "param: 2.06913808111479e-05 mean_score: 0.68\n",
      "param: 4.281332398719396e-05 mean_score: 0.65625\n",
      "param: 8.858667904100833e-05 mean_score: 0.67\n",
      "param: 0.00018329807108324357 mean_score: 0.665\n",
      "param: 0.000379269019073225 mean_score: 0.69625\n",
      "param: 0.0007847599703514606 mean_score: 0.71375\n",
      "param: 0.001623776739188721 mean_score: 0.7225\n",
      "param: 0.003359818286283781 mean_score: 0.72875\n",
      "param: 0.0069519279617756054 mean_score: 0.655\n",
      "param: 0.01438449888287663 mean_score: 0.74125\n",
      "param: 0.029763514416313162 mean_score: 0.715\n",
      "param: 0.06158482110660261 mean_score: 0.7075\n",
      "param: 0.1274274985703132 mean_score: 0.68625\n",
      "param: 0.26366508987303555 mean_score: 0.64625\n",
      "param: 0.5455594781168515 mean_score: 0.6175\n",
      "param: 1.1288378916846884 mean_score: 0.4875\n",
      "param: 2.3357214690901213 mean_score: 0.3075\n",
      "param: 4.832930238571752 mean_score: 0.1875\n",
      "param: 10.0 mean_score: 0.1225\n",
      "\n",
      "The best parameter is 0.01438 with a score of 0.7412\n"
     ]
    }
   ],
   "source": [
    "# Naive GridSearch strategy with LinUCB to find alpha\n",
    "\n",
    "# generate 20 numbers for alpha between 10^-5 to 10^1\n",
    "alphas = np.logspace(-5,1,20)\n",
    "\n",
    "# set grid parameters with alphas\n",
    "grid_parameters = {'narms': 10, 'ndims': 10, 'param_range': alphas,'rounds': 800}\n",
    "\n",
    "# create gridsearch object with strategy and scoring function\n",
    "grid_linucb = GridSearchMAB(mab=LinUCB, param_grid=grid_parameters, scoring=offlineEvaluate, strategy='naive',verbose=1)\n",
    "\n",
    "# run gridsearch on provided data\n",
    "grid_linucb.fit(arms,rewards,contexts)\n",
    "\n",
    "# best alpha for LinUCB\n",
    "print(\"\\nThe best parameter is {0.best_param_:.4g} with a score of {0.best_score_:.4g}\".format(grid_linucb))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 418
    },
    "colab_type": "code",
    "id": "zumGhffqOiHQ",
    "outputId": "c5afad64-939c-4384-e3b6-5b7f9d81fae6"
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1280x384 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting gridsearch results\n",
    "fig, ax = plt.subplots(1, 2, figsize=(10,3), squeeze=False)\n",
    "plt.subplot(1,2,1)\n",
    "plt.plot(grid_linucb.results_['params'][0:10],grid_linucb.results_['mean_score'][0:10])\n",
    "plt.title('First 10 alpha')\n",
    "plt.xlabel('LinUCB $alpha$')\n",
    "plt.ylabel('Average reward')\n",
    "plt.subplot(1,2,2)\n",
    "plt.plot(grid_linucb.results_['params'],grid_linucb.results_['mean_score'])\n",
    "plt.title('All alpha')\n",
    "plt.xlabel('LinUCB $alpha$')\n",
    "plt.ylabel('Average reward')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "B2TzFwPPTape"
   },
   "source": [
    "Similarly, we can perform gridsearch for LinThompson using same `GridSearchMAB` class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 397
    },
    "colab_type": "code",
    "id": "xyGIDQP1edOs",
    "outputId": "6cb9ab8e-abce-4795-bc69-e2c598c96966"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "param: 1e-05 mean_score: 0.45625\n",
      "param: 2.06913808111479e-05 mean_score: 0.44375\n",
      "param: 4.281332398719396e-05 mean_score: 0.4325\n",
      "param: 8.858667904100833e-05 mean_score: 0.43125\n",
      "param: 0.00018329807108324357 mean_score: 0.42125\n",
      "param: 0.000379269019073225 mean_score: 0.44875\n",
      "param: 0.0007847599703514606 mean_score: 0.44\n",
      "param: 0.001623776739188721 mean_score: 0.42875\n",
      "param: 0.003359818286283781 mean_score: 0.425\n",
      "param: 0.0069519279617756054 mean_score: 0.415\n",
      "param: 0.01438449888287663 mean_score: 0.43375\n",
      "param: 0.029763514416313162 mean_score: 0.41875\n",
      "param: 0.06158482110660261 mean_score: 0.41375\n",
      "param: 0.1274274985703132 mean_score: 0.435\n",
      "param: 0.26366508987303555 mean_score: 0.48625\n",
      "param: 0.5455594781168515 mean_score: 0.37125\n",
      "param: 1.1288378916846884 mean_score: 0.30125\n",
      "param: 2.3357214690901213 mean_score: 0.26125\n",
      "param: 4.832930238571752 mean_score: 0.09\n",
      "param: 10.0 mean_score: 0.2075\n",
      "\n",
      "The best parameter is 0.2637 with a score of 0.4863\n"
     ]
    }
   ],
   "source": [
    "# Naive GridSearch strategy with LinThompson to find hyperparameter v\n",
    "\n",
    "# generate 20 numbers for alpha between 10^-5 to 10^1\n",
    "vparams = np.logspace(-5,1,20)\n",
    "\n",
    "# set grid parameters with alphas\n",
    "grid_parameters = {'narms': 10, 'ndims': 10, 'param_range': vparams,'rounds': 800}\n",
    "\n",
    "# create gridsearch object with strategy and scoring function\n",
    "grid_linthompson = GridSearchMAB(mab=LinThompson, param_grid=grid_parameters, scoring=offlineEvaluate, strategy='naive',verbose=1)\n",
    "\n",
    "# run gridsearch on provided data\n",
    "grid_linthompson.fit(arms,rewards,contexts)\n",
    "\n",
    "# best v for LinThompson\n",
    "print(\"\\nThe best parameter is {0.best_param_:.4g} with a score of {0.best_score_:.4g}\".format(grid_linthompson))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 420
    },
    "colab_type": "code",
    "id": "u0fy3JfdUz8k",
    "outputId": "2f5453d9-aba1-4774-aa6c-15153d36352e"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1280x384 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting gridsearch results\n",
    "fig, ax = plt.subplots(1, 2, figsize=(10,3), squeeze=False)\n",
    "plt.subplot(1,2,1)\n",
    "plt.plot(grid_linthompson.results_['params'][0:10],grid_linthompson.results_['mean_score'][0:10])\n",
    "plt.title('First 10 $v$ params')\n",
    "plt.xlabel('LinThompson $v$')\n",
    "plt.ylabel('Average reward')\n",
    "plt.subplot(1,2,2)\n",
    "plt.plot(grid_linthompson.results_['params'],grid_linthompson.results_['mean_score'])\n",
    "plt.title('All $v$ params')\n",
    "plt.xlabel('LinThompson $v$')\n",
    "plt.ylabel('Average reward')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "piCXvQRjbctX"
   },
   "source": [
    "Moreover, this class is flexible enough to run GridSearch strategies to find the most optimised hyperparameter for Epsilon Greedy and UCB MAB implementations. It can be enhanced easily to support MAB algorithms with more than 1 hyperparameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 35
    },
    "colab_type": "code",
    "id": "xL2auv1Eg-pN",
    "outputId": "bd04f429-4779-4a3d-9fd8-2cdcebcefa75"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best parameter is 0.02976 with a score of 0.2625\n"
     ]
    }
   ],
   "source": [
    "# Gridsearch for UCB\n",
    "rhos = np.logspace(-5,1,20)\n",
    "param_grid = {'narms': 10, 'ndims': None, 'param_range': rhos, 'rounds': 800}\n",
    "grid_ucb = GridSearchMAB(UCB, param_grid, offlineEvaluate, strategy='naive', verbose=0)\n",
    "grid_ucb.fit(arms,rewards,contexts)\n",
    "print(\"The best parameter is {0.best_param_:.4g} with a score of {0.best_score_:.4g}\".format(grid_ucb))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 35
    },
    "colab_type": "code",
    "id": "6sPKdXxYcL9f",
    "outputId": "6576b120-89db-4920-8862-7f32c332a470"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best parameter is 0.1624 with a score of 0.1462\n"
     ]
    }
   ],
   "source": [
    "# Gridsearch for EpsGreedy\n",
    "eps = np.logspace(-5,0,20)\n",
    "param_grid = {'narms': 10, 'ndims': None, 'param_range': eps, 'rounds': 800}\n",
    "grid_epsgreedy = GridSearchMAB(EpsGreedy, param_grid, offlineEvaluate, strategy='naive', verbose=0)\n",
    "grid_epsgreedy.fit(arms,rewards,contexts)\n",
    "print(\"The best parameter is {0.best_param_:.4g} with a score of {0.best_score_:.4g}\".format(grid_epsgreedy))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "EGskwJuPbbG_"
   },
   "source": [
    "Finally, we can plot the evaluation again with the optimised hyperparameters for each algorithm as shown below"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 488
    },
    "colab_type": "code",
    "id": "V8lHdJDecrfg",
    "outputId": "690d0ccc-2ce4-47d9-9aee-c05243f04e24"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 768x512 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Evaluating algorithms for 800 rounds with optimised hyperparameters\n",
    "evaluation(T=800,params={'eps_greedy':grid_epsgreedy.best_param_, 'ucb':grid_ucb.best_param_, 'beta_thompson':[1.0,1.0], 'lin_ucb':grid_linucb.best_param_, 'lin_thompson':grid_linthompson.best_param_})"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "abhsharma_drive.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
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