[Stats_Practice]_Reinforcement_Learning_Algorithms_Comparison.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "[Stats Practice] Reinforcement Learning Algorithms Comparison",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "2sOCRLVTFS-k",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 317
        },
        "outputId": "18922c20-d5d1-421f-95c9-a9609a4dcf9d"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "def getSamplar():\n",
        "    mu=np.random.normal(0,10)\n",
        "    sd=abs(np.random.normal(5,2))\n",
        "    getSample=lambda: np.random.normal(mu,sd)\n",
        "    return getSample\n",
        "\n",
        "def e_greedy(Q, e):\n",
        "##################################################\n",
        "#\t\tYour code here\n",
        "##################################################  \n",
        "    #Q is dictionary in form (possible actions: average reward of action)\n",
        "    #e is a 0-1 scalar; Return action selected from Q based on reward and epsilon\n",
        "    #Run a probability weighed between the Q greedy (highest reward) action and a random action\n",
        "    #from the epsilon random value.\n",
        "    action_dict = Q\n",
        "    #Get probabilities for action choices\n",
        "    \n",
        "    #random_choice_probability = (e/(len(action_dict) - 1)) \n",
        "    random_choice_probability = (e/(len(action_dict))) \n",
        "    greedy_choice_probability = 1 - e + random_choice_probability\n",
        "    #Initialize index and values\n",
        "    #optimal_action_index = -1\n",
        "    optimal_action_value = max(action_dict.values())\n",
        "    #for i in action_dict:\n",
        "    #  if (action_dict[i] > optimal_action_value):\n",
        "    #        optimal_action_value = action_dict[i]\n",
        "    #        #optimal_action_index = i\n",
        "    \n",
        "    #prob dictionary creation\n",
        "    actions = list(action_dict.keys())\n",
        "    probs = []\n",
        "    #Creation of a new dictionary matching actions to probability\n",
        "    for i in action_dict:\n",
        "      if(action_dict[i] == optimal_action_value):\n",
        "          #pre_prob_dict[i] = greedy_choice_probability\n",
        "          probs.append(greedy_choice_probability)\n",
        "      else:\n",
        "        probs.append(random_choice_probability)\n",
        "          #pre_prob_dict[i] = random_choice_probability\n",
        "    probs = np.array(probs)\n",
        "    probs /= sum(probs)\n",
        "    #actions = list(pre_prob_dict.keys())\n",
        "    #probs = list(pre_prob_dict.values())\n",
        "    choice = np.random.choice(actions, 1, replace=True, p=probs)\n",
        "    return choice.item()\n",
        "\n",
        "    \n",
        "def upperConfidenceBound(Q, N, c):   \n",
        "##################################################\n",
        "#\t\tYour code here\n",
        "##################################################  \n",
        "    #Q dictionary (possible action: average reward of action)\n",
        "    ##N dictionary (possible action: number of times action was taken)\n",
        "    #C is some scalar\n",
        "    #Return an action of Q based on algorithm\n",
        "    # #Q is dictionary in form (possible actions: average reward of action)\n",
        "    action_dict = Q\n",
        "    frequency_dict = N\n",
        "    maximized_expression_value = 0\n",
        "    choice = 0\n",
        "    uc_dict = {}\n",
        "    for action in action_dict:\n",
        "      #if ((action_dict[action] + c * np.sqrt(np.log(sum(frequency_dict.values()) + 1)/(frequency_dict[action]))) > maximized_expression_value):\n",
        "      uc_dict[action] = action_dict[action] + c*np.sqrt(np.log(sum(frequency_dict.values()) + 1)/(frequency_dict[action] + 1))\n",
        "      #choice = action\n",
        "    choice = max(uc_dict, key = uc_dict.get)\n",
        "    return choice\n",
        "\n",
        "\n",
        "def updateQN(action, reward, Q, N):\n",
        "##################################################\n",
        "#\t\tYour code here\n",
        "##################################################  \n",
        "    #Action = action from Q key taken\n",
        "    #Reward =  rewal reward retrieved, Q and N are inherite (possible action: number of times action was taken).\n",
        "    #Return a tuple of updated Q and N.\n",
        "    qCopy = Q\n",
        "    nCopy = N\n",
        "    updatedQ = {}\n",
        "    updatedN = {}\n",
        "    #updating number of actions\n",
        "    #\n",
        "    #qCopy[action] = ((qCopy[action] * (nCopy[action] - 1)) + reward)/nCopy[action]\n",
        "    for new_action in N:\n",
        "      if (new_action == action):\n",
        "        #if (qCopy[new_action] != 0):\n",
        "        updatedN[new_action] = N[new_action] + 1\n",
        "      else:\n",
        "        updatedN[new_action] = N[new_action] \n",
        "\n",
        "    for new_action in Q:\n",
        "      if (new_action == action):\n",
        "        #if (qCopy[new_action] != 0):\n",
        "        updatedQ[new_action] = (((Q[new_action] * (updatedN[new_action] - 1)) + reward) / updatedN[new_action])\n",
        "      else:\n",
        "        updatedQ[new_action] = Q[new_action]\n",
        "\n",
        "    tuple_qn = (updatedQ, updatedN)\n",
        "    return tuple_qn\n",
        "\n",
        "\n",
        "def decideMultipleSteps(Q, N, policy, bandit, maxSteps):\n",
        "##################################################\n",
        "#\t\tYour code here\n",
        "##################################################  \n",
        "    #Q and N are inherited from other\n",
        "    #Policy likely  reflects choice of formula (using greedy or ucb)\n",
        "    #Bandit is a function generating reward of action, based on getSampler\n",
        "    #Policy and bandit are essentially just lambda functions running our helper\n",
        "    #MaxSteps follows some iteration rule\n",
        "    #A scalar showing how many steps you have\n",
        "    #dictionaryOfDictionaries\n",
        "    #update Q qand N\n",
        "    #generic\n",
        "    action_taken = policy(Q, N)\n",
        "    bandit_value = bandit(action_taken)\n",
        "    updatedQN = updateQN(action_taken, bandit_value, Q, N)\n",
        "    action_reward = []\n",
        "    stepCount_Iterative = list(range(maxSteps - 1)) \n",
        "    #Multiple steps are used to tie a policy value\n",
        "    for i in stepCount_Iterative:\n",
        "      updatedQN = updateQN(action_taken, bandit_value, updatedQN[0], updatedQN[1])\n",
        "      action_reward_entry = (action_taken, bandit_value)\n",
        "      action_reward.append(action_reward_entry)\n",
        "      iterative_Q = updatedQN[0]\n",
        "      #print(iterative_Q)\n",
        "      iterative_N = updatedQN[1]\n",
        "      #print(iterative_N)\n",
        "      action_taken = policy(iterative_Q,iterative_N)\n",
        "      bandit_value = bandit(action_taken)\n",
        "    \n",
        "    #how does policy and bandit work, am I supposed to store their values?\n",
        "    actionReward = action_reward\n",
        "    stepsDict = {}\n",
        "    stepsDict[\"Q\"] = iterative_Q\n",
        "    stepsDict[\"N\"] = iterative_N\n",
        "    stepsDict[\"actionReward\"] =action_reward\n",
        "    return  stepsDict\n",
        "    #a dictionary containing “Q”, “N”, and “actionReward”. The Q and N are updated Q and N. ActionReward is a list that records your action and reward of\n",
        "    #each step. It contains the tuples (action, reward).\n",
        "\n",
        "\n",
        "def plotMeanReward(actionReward,label):\n",
        "    maxSteps=len(actionReward)\n",
        "    reward=[reward for (action,reward) in actionReward]\n",
        "    meanReward=[sum(reward[:(i+1)])/(i+1) for i in range(maxSteps)]\n",
        "    plt.plot(range(maxSteps), meanReward, linewidth=0.9, label=label)\n",
        "    plt.xlabel('Steps')\n",
        "    plt.ylabel('Average Reward')\n",
        "\n",
        "def main():\n",
        "    np.random.seed(2020)\n",
        "    K=10\n",
        "    maxSteps=1000\n",
        "    Q={k:0 for k in range(K)}\n",
        "    N={k:0 for k in range(K)}\n",
        "    testBed={k:getSamplar() for k in range(K)}\n",
        "    bandit=lambda action: testBed[action]()\n",
        "    \n",
        "    policies={}\n",
        "    policies[\"e-greedy-0.5\"]=lambda Q, N: e_greedy(Q, 0.5)\n",
        "    policies[\"e-greedy-0.1\"]=lambda Q, N: e_greedy(Q, 0.1)\n",
        "    policies[\"UCB-2\"]=lambda Q, N: upperConfidenceBound(Q, N, 2)\n",
        "    policies[\"UCB-20\"]=lambda Q, N: upperConfidenceBound(Q, N, 20)\n",
        "    \n",
        "    allResults = {name: decideMultipleSteps(Q, N, policy, bandit, maxSteps) for (name, policy) in policies.items()}\n",
        "    \n",
        "    for name, result in allResults.items():\n",
        "         plotMeanReward(allResults[name]['actionReward'], label=name)\n",
        "    plt.legend(bbox_to_anchor=(0., 1.02, 1., .102), loc='lower left',ncol=2, mode=\"expand\", borderaxespad=0.)\n",
        "    plt.show()\n",
        "    \n",
        "\n",
        "\n",
        "if __name__=='__main__':\n",
        "    main()\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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mI1a9Ax2NYktPt47r9aLcbpTTheF2oeyHUC0mYtDZCmYc/MP2DAriEYiFINoBkSCEaiBh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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vrJ8_5F-a3NY"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_dpUvW76Gs2Q"
      },
      "source": [
        "def getSamplar():\n",
        "    mu=np.random.normal(0,10)\n",
        "    sd=abs(np.random.normal(5,2))\n",
        "    getSample=lambda: np.random.normal(mu,sd)\n",
        "    #return getSample()\n",
        "    return getSample"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rctAonTWWPGu",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        },
        "outputId": "5f8b2afc-4694-4df9-b9a8-e08e2f17626f"
      },
      "source": [
        "    mu=np.random.normal(0,10)\n",
        "    sd=abs(np.random.normal(5,2))\n",
        "    getSample=lambda: np.random.normal(mu,sd)\n",
        "    print(mu)\n",
        "    print(sd)\n",
        "    getSample()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "-4.521334172143789\n",
            "7.688106969368345\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "-12.960227127436173"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 53
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dY1jCi0rF5JX",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "43318511-d545-4d49-b4f1-a6432dadaef1"
      },
      "source": [
        "    np.random.seed(2020)\n",
        "    K=10\n",
        "    maxSteps=1000\n",
        "    Q={k:0 for k in range(K)}\n",
        "    N={k:0 for k in range(K)}\n",
        "\n",
        "    probs = {}\n",
        "    probs[0] = 3\n",
        "    probs\n",
        "  "
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{0: 3}"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 54
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8Ia05rnYFi-6"
      },
      "source": [
        "def e_greedy(Q, e):\n",
        "##################################################\n",
        "#\t\tYour code here\n",
        "##################################################  \n",
        "    #Q is dictionary in form (possible actions: average reward of action)\n",
        "    #e is a 0-1 scalar; Return action selected from Q based on reward and epsilon\n",
        "    #Run a probability weighed between the Q greedy (highest reward) action and a random action\n",
        "    #from the epsilon random value.\n",
        "    action_dict = Q\n",
        "    #Get probabilities for action choices\n",
        "    greedy_choice_probability = 1 - e\n",
        "    random_choice_probability = (e/(len(action_dict) - 1)) \n",
        "    #Initialize index and values\n",
        "    #optimal_action_index = -1\n",
        "    optimal_action_value = max(action_dict.values())\n",
        "    #for i in action_dict:\n",
        "    #  if (action_dict[i] > optimal_action_value):\n",
        "    #        optimal_action_value = action_dict[i]\n",
        "    #        #optimal_action_index = i\n",
        "    \n",
        "    #prob dictionary creation\n",
        "    actions = list(action_dict.keys())\n",
        "    probs = []\n",
        "    #Creation of a new dictionary matching actions to probability\n",
        "    for i in action_dict:\n",
        "      if(action_dict[i] == optimal_action_value):\n",
        "          #pre_prob_dict[i] = greedy_choice_probability\n",
        "          probs.append(greedy_choice_probability)\n",
        "      else:\n",
        "        probs.append(random_choice_probability)\n",
        "          #pre_prob_dict[i] = random_choice_probability\n",
        "    probs = np.array(probs)\n",
        "    probs /= sum(probs)\n",
        "    #actions = list(pre_prob_dict.keys())\n",
        "    #probs = list(pre_prob_dict.values())\n",
        "    choice = np.random.choice(actions, 1, replace=True, p=probs)\n",
        "    return choice.item()\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rQQ7MHgDO0U2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        },
        "outputId": "1b689104-e189-4aca-baf4-b838ae523673"
      },
      "source": [
        "    utilityTable={1:2000, 2:-500, 3:100, 4:1000, 5:0}\n",
        "    #print(Q)\n",
        "    e = .5\n",
        "    print(e_greedy(utilityTable, .5))\n",
        "    action_dict = utilityTable\n",
        "    #Get probabilities for action choices\n",
        "    greedy_choice_probability = 1 - e\n",
        "    random_choice_probability = (e/(len(action_dict) - 1)) \n",
        "    #Initialize index and values\n",
        "    #optimal_action_index = -1\n",
        "    optimal_action_value = max(action_dict.values())\n",
        "    #for i in action_dict:\n",
        "    #  if (action_dict[i] > optimal_action_value):\n",
        "    #        optimal_action_value = action_dict[i]\n",
        "    #        #optimal_action_index = i\n",
        "    \n",
        "    #prob dictionary creation\n",
        "    actions = list(action_dict.keys())\n",
        "    probs = {}\n",
        "    #Creation of a new dictionary matching actions to probability\n",
        "    for i in actions:\n",
        "      if(action_dict[i] == optimal_action_value):\n",
        "          #pre_prob_dict[i] = greedy_choice_probability\n",
        "          probs[i] = (greedy_choice_probability)\n",
        "      else:\n",
        "        probs[i] = (random_choice_probability)\n",
        "          #pre_prob_dict[i] = random_choice_probability\n",
        "        \n",
        "    print(probs)\n",
        "    choice = np.random.choice(actions, 1, replace=True, p=list(probs.values()))\n",
        "    sum(probs.values())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "5\n",
            "{1: 0.5, 2: 0.125, 3: 0.125, 4: 0.125, 5: 0.125}\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.0"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 56
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2vpTNefZ8iE-",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        },
        "outputId": "19a20ac4-ef6d-4a27-dd0e-38dd31594930"
      },
      "source": [
        "    utilityTable={1:2000, 2:-500, 3:100, 4:1000, 5:0}\n",
        "    print(min(utilityTable.values()))\n",
        "    optimal_action_index = 1\n",
        "    greedy_choice_probability = .85\n",
        "    random_choice_probability = .15/4\n",
        "\n",
        "    actions = list(utilityTable.keys())\n",
        "    probs = {}\n",
        "    #Creation of a new dictionary matching actions to probability\n",
        "    for i in actions:\n",
        "      if(i == optimal_action_index):\n",
        "          #pre_prob_dict[i] = greedy_choice_probability\n",
        "          probs[i] = (greedy_choice_probability)\n",
        "      else:\n",
        "        probs[i] = random_choice_probability\n",
        "          #pre_prob_dict[i] = random_choice_probability\n",
        "    \n",
        "    #actions = list(pre_prob_dict.keys())\n",
        "    #probs = list(pre_prob_dict.values())\n",
        "    print(probs)\n",
        "    choice = np.random.choice(actions, 1, replace=True, p=list(probs.values()))\n",
        "    "
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "-500\n",
            "{1: 0.85, 2: 0.0375, 3: 0.0375, 4: 0.0375, 5: 0.0375}\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7n9r9ygVePI1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "51bf8a16-0001-4233-86d8-782cf0cefe1e"
      },
      "source": [
        "    c = 2\n",
        "    action_dict = utilityTable\n",
        "    frequency_dict = otherTable\n",
        "    maximized_expression_value = 0\n",
        "    choice = 0\n",
        "    for action in action_dict:\n",
        "      if (action_dict[action] + c * np.sqrt((2*np.log(action)/(frequency_dict[action]))) > maximized_expression_value):\n",
        "        maximized_expression_value = action_dict[action] + c*np.sqrt(2*np.log(action)/frequency_dict[action] + 1)\n",
        "        choice = action\n",
        "    choice"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 58
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rk8p2ebZFd0Q"
      },
      "source": [
        "def upperConfidenceBound(Q, N, c):   \n",
        "##################################################\n",
        "#\t\tYour code here\n",
        "##################################################  \n",
        "    #Q dictionary (possible action: average reward of action)\n",
        "    ##N dictionary (possible action: number of times action was taken)\n",
        "    #C is some scalar\n",
        "    #Return an action of Q based on algorithm\n",
        "    # #Q is dictionary in form (possible actions: average reward of action)\n",
        "    action_dict = Q\n",
        "    frequency_dict = N\n",
        "    maximized_expression_value = 0\n",
        "    choice = 0\n",
        "    uc_dict = {}\n",
        "    for action in action_dict:\n",
        "      #if ((action_dict[action] + c * np.sqrt(np.log(sum(frequency_dict.values()) + 1)/(frequency_dict[action]))) > maximized_expression_value):\n",
        "      uc_dict[action] = action_dict[action] + c*np.sqrt(np.log(sum(frequency_dict.values()) + 1)/(frequency_dict[action] + 1))\n",
        "      #choice = action\n",
        "    choice = max(uc_dict, key = uc_dict.get)\n",
        "    return choice\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LukTm9oPFeBL"
      },
      "source": [
        "def updateQN(action, reward, Q, N):\n",
        "##################################################\n",
        "#\t\tYour code here\n",
        "##################################################  \n",
        "    #Action = action from Q key taken\n",
        "    #Reward =  rewal reward retrieved, Q and N are inherite (possible action: number of times action was taken).\n",
        "    #Return a tuple of updated Q and N.\n",
        "    qCopy = Q\n",
        "    nCopy = N\n",
        "    updatedQ = {}\n",
        "    updatedN = {}\n",
        "    #updating number of actions\n",
        "    #\n",
        "    #qCopy[action] = ((qCopy[action] * (nCopy[action] - 1)) + reward)/nCopy[action]\n",
        "    for new_action in N:\n",
        "      if (new_action == action):\n",
        "        #if (qCopy[new_action] != 0):\n",
        "        updatedN[new_action] = N[new_action] + 1\n",
        "      else:\n",
        "        updatedN[new_action] = N[new_action] \n",
        "\n",
        "    for new_action in Q:\n",
        "      if (new_action == action):\n",
        "        #if (qCopy[new_action] != 0):\n",
        "        updatedQ[new_action] = (((Q[new_action] * (updatedN[new_action] - 1)) + reward) / updatedN[new_action])\n",
        "      else:\n",
        "        updatedQ[new_action] = Q[new_action]\n",
        "\n",
        "    \n",
        "\n",
        "        #N is to be updated when Action is taken, increasing the times taken\n",
        "        #Q is affected by the average reward? Makes sense, action is taken and a new value was generated\n",
        "        #Take the average as a result.\n",
        "    \n",
        "    tuple_qn = (updatedQ, updatedN)\n",
        "    return tuple_qn\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ksZ5M1DDdF98",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        },
        "outputId": "5df29ad9-483a-43dd-849c-d1d46e88e1a7"
      },
      "source": [
        "    utilityTable={1:2000, 2:-500, 3:100, 4:1000, 5:0}\n",
        "    otherTable={1:5, 2:12, 3:5, 4:20, 5:24}\n",
        " \n",
        "    print(upperConfidenceBound(utilityTable, otherTable, 2))\n",
        "    print(utilityTable)\n",
        "    print(otherTable)\n",
        "    "
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "1\n",
            "{1: 2000, 2: -500, 3: 100, 4: 1000, 5: 0}\n",
            "{1: 5, 2: 12, 3: 5, 4: 20, 5: 24}\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fzBC_NaoFZus"
      },
      "source": [
        "def decideMultipleSteps(Q, N, policy, bandit, maxSteps):\n",
        "##################################################\n",
        "#\t\tYour code here\n",
        "##################################################  \n",
        "    #Q and N are inherited from other\n",
        "    #Policy likely  reflects choice of formula (using greedy or ucb)\n",
        "    #Bandit is a function generating reward of action, based on getSampler\n",
        "    #Policy and bandit are essentially just lambda functions running our helper\n",
        "    #MaxSteps follows some iteration rule\n",
        "    #A scalar showing how many steps you have\n",
        "    #dictionaryOfDictionaries\n",
        "    #update Q qand N\n",
        "    #generic\n",
        "    action_taken = policy(Q, N)\n",
        "    bandit_value = bandit(action_taken)\n",
        "    updatedQN = updateQN(action_taken, bandit_value, Q, N)\n",
        "    action_reward = []\n",
        "    stepCount_Iterative = list(range(maxSteps - 1)) \n",
        "    #Multiple steps are used to tie a policy value\n",
        "    for i in stepCount_Iterative:\n",
        "      updatedQN = updateQN(action_taken, bandit_value, updatedQN[0], updatedQN[1])\n",
        "      action_reward_entry = (action_taken, bandit_value)\n",
        "      action_reward.append(action_reward_entry)\n",
        "      iterative_Q = updatedQN[0]\n",
        "      #print(iterative_Q)\n",
        "      iterative_N = updatedQN[1]\n",
        "      #print(iterative_N)\n",
        "      action_taken = policy(iterative_Q,iterative_N)\n",
        "      bandit_value = bandit(action_taken)\n",
        "    \n",
        "    #how does policy and bandit work, am I supposed to store their values?\n",
        "    actionReward = action_reward\n",
        "    stepsDict = {}\n",
        "    stepsDict[\"Q\"] = iterative_Q\n",
        "    stepsDict[\"N\"] = iterative_N\n",
        "    stepsDict[\"actionReward\"] =action_reward\n",
        "    return  stepsDict\n",
        "    #a dictionary containing “Q”, “N”, and “actionReward”. The Q and N are updated Q and N. ActionReward is a list that records your action and reward of\n",
        "    #each step. It contains the tuples (action, reward).\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Zp8HbZwcFZ4w"
      },
      "source": [
        "def plotMeanReward(actionReward,label):\n",
        "    maxSteps=len(actionReward)\n",
        "    reward=[reward for (action,reward) in actionReward]\n",
        "    meanReward=[sum(reward[:(i+1)])/(i+1) for i in range(maxSteps)]\n",
        "    plt.plot(range(maxSteps), meanReward, linewidth=0.9, label=label)\n",
        "    plt.xlabel('Steps')\n",
        "    plt.ylabel('Average Reward')"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "13yarxcl4n44",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "42cf0b7b-3e97-4c29-cb03-5f934072a5e6"
      },
      "source": [
        "    np.random.seed(2020)\n",
        "    K=10\n",
        "    testBed={k:getSamplar() for k in range(K)}\n",
        "    testBed\n",
        "    bandit=lambda action: testBed[action]()\n",
        "    bandit(1)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "-3.5793533556053108"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 64
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NJo5RQNeT5sC",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "bd6a3a6c-fbd8-489f-fa1f-d960ea4e5dbd"
      },
      "source": [
        "K = 10\n",
        "Q={k:0 for k in range(K)}\n",
        "N={k:0 for k in range(K)}\n",
        "print(Q)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "{0: 0, 1: 0, 2: 0, 3: 0, 4: 0, 5: 0, 6: 0, 7: 0, 8: 0, 9: 0}\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ESqW_u3NFWE0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 317
        },
        "outputId": "a25b80a4-34ea-4add-e434-b0b593e6e819"
      },
      "source": [
        "def main():\n",
        "    np.random.seed(2020)\n",
        "    K=10\n",
        "    maxSteps=1000\n",
        "    Q={k:0 for k in range(K)}\n",
        "    N={k:0 for k in range(K)}\n",
        "    testBed={k:getSamplar() for k in range(K)}\n",
        "    bandit=lambda action: testBed[action]()\n",
        "    policies={}\n",
        "    policies[\"e-greedy-0.5\"]=lambda Q, N: e_greedy(Q, 0.5)\n",
        "    policies[\"e-greedy-0.1\"]=lambda Q, N: e_greedy(Q, 0.1)\n",
        "    policies[\"UCB-2\"]=lambda Q, N: upperConfidenceBound(Q, N, 2)\n",
        "    policies[\"UCB-20\"]=lambda Q, N: upperConfidenceBound(Q, N, 20)\n",
        "    \n",
        "    allResults = {name: decideMultipleSteps(Q, N, policy, bandit, maxSteps) for (name, policy) in policies.items()}\n",
        "    \n",
        "    for name, result in allResults.items():\n",
        "         plotMeanReward(allResults[name]['actionReward'], label=name)\n",
        "    plt.legend(bbox_to_anchor=(0., 1.02, 1., .102), loc='lower left',ncol=2, mode=\"expand\", borderaxespad=0.)\n",
        "    plt.show()\n",
        "    \n",
        "\n",
        "\n",
        "if __name__=='__main__':\n",
        "    main()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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I121Hx2LYMjOt83q9KLcb5XRhuF0ou1SLIMmh7za8Ao9eAOffD1MuHexoxFFMa02yo4NE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\nAwcHMzNr4OBgZmYN/g9Euk1bYtRCuQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}