RL_BanditsCode.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# **Recommendation System**"
      ],
      "metadata": {
        "id": "PzybQo2G2gE3"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Done by:\n",
        "\n",
        "1. 18PD05 - Bharathi A\n",
        "2. 18PD33 - Shreenidhi N"
      ],
      "metadata": {
        "id": "uNpIaFd12k39"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import os\n",
        "os.chdir('/content/drive/MyDrive/RL/Package3/Bandits/bandits/single')"
      ],
      "metadata": {
        "id": "hDzBN7D2Kj5s"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "e-TNOAd3KjRM"
      },
      "outputs": [],
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "\n",
        "sns.set_theme()"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/drive')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pIOrFZxrK2WY",
        "outputId": "68c7b49e-a1b5-4ab3-b343-bc79cf7c88d3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mounted at /content/drive\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6WCGyAcBKjRP"
      },
      "source": [
        "## Preprocessing Movielens data"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3pmmCn03KjRQ",
        "outputId": "573db68f-f785-4ae2-a9fd-105d6df9b19e"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "reading movielens 1m data\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/pandas/util/_decorators.py:311: ParserWarning: Falling back to the 'python' engine because the 'c' engine does not support regex separators (separators > 1 char and different from '\\s+' are interpreted as regex); you can avoid this warning by specifying engine='python'.\n",
            "  return func(*args, **kwargs)\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "   MovieID                               Title                        Genres\n",
            "0        1                    Toy Story (1995)   Animation|Children's|Comedy\n",
            "1        2                      Jumanji (1995)  Adventure|Children's|Fantasy\n",
            "2        3             Grumpier Old Men (1995)                Comedy|Romance\n",
            "3        4            Waiting to Exhale (1995)                  Comedy|Drama\n",
            "4        5  Father of the Bride Part II (1995)                        Comedy\n",
            "   MovieID                               Title                        Genres  \\\n",
            "0        1                    Toy Story (1995)   Animation|Children's|Comedy   \n",
            "1        2                      Jumanji (1995)  Adventure|Children's|Fantasy   \n",
            "2        3             Grumpier Old Men (1995)                Comedy|Romance   \n",
            "3        4            Waiting to Exhale (1995)                  Comedy|Drama   \n",
            "4        5  Father of the Bride Part II (1995)                        Comedy   \n",
            "\n",
            "   Action  Adventure  Animation  Children's  Comedy  Crime  Documentary  ...  \\\n",
            "0   False      False       True        True    True  False        False  ...   \n",
            "1   False       True      False        True   False  False        False  ...   \n",
            "2   False      False      False       False    True  False        False  ...   \n",
            "3   False      False      False       False    True  False        False  ...   \n",
            "4   False      False      False       False    True  False        False  ...   \n",
            "\n",
            "   Fantasy  Film-Noir  Horror  Musical  Mystery  Romance  Sci-Fi  Thriller  \\\n",
            "0    False      False   False    False    False    False   False     False   \n",
            "1     True      False   False    False    False    False   False     False   \n",
            "2    False      False   False    False    False     True   False     False   \n",
            "3    False      False   False    False    False    False   False     False   \n",
            "4    False      False   False    False    False    False   False     False   \n",
            "\n",
            "     War  Western  \n",
            "0  False    False  \n",
            "1  False    False  \n",
            "2  False    False  \n",
            "3  False    False  \n",
            "4  False    False  \n",
            "\n",
            "[5 rows x 21 columns]\n"
          ]
        }
      ],
      "source": [
        "print('reading movielens 1m data')\n",
        "ratings = pd.read_csv('data/ml-1m/ratings.dat', sep='::', names=['UserID','MovieID','Rating','Timestamp'], encoding = \"ISO-8859-1\")\n",
        "movies = pd.read_csv('data/ml-1m/movies.dat', sep='::', names=['MovieID','Title','Genres'], encoding = \"ISO-8859-1\")\n",
        "users = pd.read_csv('data/ml-1m/users.dat', sep='::', names=['UserID','Gender','Age','Occupation', 'Zip'], encoding = \"ISO-8859-1\")\n",
        "#ratings = pd.read_csv('../data/ml-1m/ratings.dat', sep=':', usecols=range(0,5,2), names=['UserID','MovieID','Rating'], encoding = \"ISO-8859-1\")\n",
        "#movies = pd.read_csv('../data/ml-1m/movies.dat', sep=':', usecols=range(0,5,2), names=['MovieID','Title','Genres'], encoding = \"ISO-8859-1\")\n",
        "#users = pd.read_csv('../data/ml-1m/users.dat', sep=':', usecols=range(0,7,2), names=['UserID','Gender','Age','Occupation'], encoding = \"ISO-8859-1\")\n",
        "\n",
        "#One hot encoding the genres\n",
        "movies = movies.join(movies['Genres'].str.get_dummies().astype(bool))\n",
        "print(movies.head())\n",
        "movies.drop('Genres', inplace=True, axis=1)\n",
        "ratings['Liked'] = ratings['Rating'].apply(lambda x: 1 if x == 5 else 0)"
      ]
    },
    {
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      "execution_count": null,
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          "base_uri": "https://localhost:8080/"
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        "id": "9regs7E7KjRR",
        "outputId": "553e03e5-429e-4142-fce9-c0c435da1ead"
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      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Int64Index([2858, 260, 1196, 1210, 480, 2028, 589, 2571, 1270, 593], dtype='int64')\n"
          ]
        }
      ],
      "source": [
        "top10ids = ratings['MovieID'].value_counts().head(10)\n",
        "most_rated = movies.loc[movies['MovieID'].isin(top10ids.index)]\n",
        "print(top10ids.index)"
      ]
    },
    {
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              "         UserID  MovieID  Rating  Timestamp  Liked\n",
              "22            1     1270       5  978300055      1\n",
              "44            1      260       4  978300760      0\n",
              "48            1     2028       5  978301619      1\n",
              "64            2     1210       4  978298151      0\n",
              "98            2      589       4  978299773      0\n",
              "...         ...      ...     ...        ...    ...\n",
              "999959     6040     1196       3  956715455      0\n",
              "999982     6040     2571       4  997454126      0\n",
              "1000033    6040     1210       2  956715805      0\n",
              "1000074    6040     1270       3  997453960      0\n",
              "1000200    6040     2028       5  956704519      1\n",
              "\n",
              "[28017 rows x 5 columns]"
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      ],
      "source": [
        "ratings_top10 = ratings.loc[ratings['MovieID'].isin(top10ids.index)]\n",
        "ratings_top10"
      ]
    },
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              "      UserID Gender  Age  Occupation    Zip\n",
              "0          1      F    1          10  48067\n",
              "1          2      M   56          16  70072\n",
              "2          3      M   25          15  55117\n",
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              "...      ...    ...  ...         ...    ...\n",
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          },
          "metadata": {},
          "execution_count": 7
        }
      ],
      "source": [
        "users_top10 = users.loc[users['UserID'].isin(ratings_top10['UserID'])]\n",
        "users_top10"
      ]
    },
    {
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          },
          "metadata": {},
          "execution_count": 8
        }
      ],
      "source": [
        "data = pd.merge(ratings_top10, users_top10, on='UserID').sample(frac=1,random_state=5).reset_index(drop=True)\n",
        "data"
      ]
    },
    {
      "cell_type": "code",
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        "data['Liked'].unique()"
      ],
      "metadata": {
        "id": "Izma7cm-dINj",
        "outputId": "0271fe17-cac8-4da3-dd08-48b8fcfcb233",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 1])"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kP4q7lo0KjRT"
      },
      "source": [
        "Bandit implementations require knowledge of time horizon, number of arms (movies) k, and the reward function for taking action A at time step t. This can influence the performance of the algorithms as the value updates depend on the time horizon. THe time horizon can vary between 0 and the length of dataset, however the expected time horizon is length of dataset / k."
      ]
    },
    {
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            " [0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
            " [0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
            " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
            " [0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
            " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
            " [0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
            " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 1. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
            " [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 0. 1.]\n",
            " [0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
            " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 1. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 0. 1. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 1. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n",
            " [1. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
            " [0. 1. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 1. 0. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]\n",
            " [0. 0. 0. 0. 0. 0. 0. 1. 0. 0.]]\n"
          ]
        }
      ],
      "source": [
        "horizon = len(data.index)*1\n",
        "k = len(top10ids.index)\n",
        "M = 10\n",
        "\n",
        "def reward(t,A):\n",
        "    t = t % len(data.index)\n",
        "    if data['MovieID'].iloc[t] == top10ids.index[A]:\n",
        "        return data['Liked'].iloc[t]\n",
        "    return None\n",
        "\n",
        "# Experts 100 random distributions f: age group -> movie\n",
        "expert = {}\n",
        "diag = np.zeros((k,k))\n",
        "np.fill_diagonal(diag, 1)\n",
        "diag = np.tile(diag,(M,1))\n",
        "for age in data['Age'].unique():\n",
        "    new_ks = diag.copy()\n",
        "    expert[age] = new_ks\n",
        "    np.random.shuffle(expert[age])\n",
        "\n",
        "def advice(t):\n",
        "    t = t % len(data.index)\n",
        "    return expert[data['Age'].iloc[t]]\n",
        "\n",
        "print(expert[25])"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# **2. Experiments**"
      ],
      "metadata": {
        "id": "8jUYx93SXriM"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# a. UCB"
      ],
      "metadata": {
        "id": "KvNKwrWtYKZW"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Policy\n",
        "def UCB_next_action(t, Q, N, c):\n",
        "    min_action = np.argmin(N)\n",
        "    if N[min_action] == 0:\n",
        "        next_action = min_action\n",
        "    else:\n",
        "        next_action = np.argmax(Q+c*np.sqrt(np.log(t)/N))\n",
        "    return next_action\n",
        "\n",
        "# Value updates and step sizes\n",
        "def update_weighted_average(t, Q, arm, pulls, reward, alpha):\n",
        "    Q[arm] = Q[arm] + alpha(t,pulls)*(reward - Q[arm])\n",
        "    return Q\n",
        "\n",
        "def const_step(*_):\n",
        "    return 0.1\n",
        "\n",
        "def sample_average_step(_,pulls):\n",
        "    return (1/pulls)\n",
        "\n",
        "def time_decrease_step(t,_):\n",
        "    return (1/(t+1))\n",
        "\n",
        "# Bandit interaction\n",
        "def UCB(k,reward,horizon,c=2,step_size=sample_average_step):\n",
        "    all_rewards = []\n",
        "    Q = np.zeros(k)\n",
        "    N = np.zeros(k)\n",
        "    t_hit = 0\n",
        "    for t in range(horizon):\n",
        "        A = UCB_next_action(t_hit,Q,N,c)\n",
        "        X = reward(t,A)\n",
        "        if X is not None:\n",
        "            N[A] += 1\n",
        "            Q = update_weighted_average(t_hit,Q,A,N[A],X,step_size)\n",
        "            all_rewards.append(X)\n",
        "            t_hit += 1\n",
        "    return all_rewards"
      ],
      "metadata": {
        "id": "JB03EenuX-xV"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# b. Exp3"
      ],
      "metadata": {
        "id": "91TTBQFXYOcu"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Policy\n",
        "def exp3_next_action(S, c):\n",
        "    P = np.exp(c*S)/np.sum(np.exp(c*S))\n",
        "    return np.random.choice(len(P),p=P), P\n",
        "\n",
        "# Action weight update\n",
        "def update_importance_weighted(S,arm,reward,P):\n",
        "    S[arm] = S[arm] + reward/P[arm]\n",
        "    return S\n",
        "\n",
        "# Bandit interaction\n",
        "def Exp3(k,reward,horizon,eta):\n",
        "    all_rewards = []\n",
        "    S = np.zeros(k)\n",
        "    for t in range(horizon):\n",
        "        A, P = exp3_next_action(S, eta)\n",
        "        X = reward(t,A)\n",
        "        if X is not None:\n",
        "            S = update_importance_weighted(S,A,X,P)\n",
        "            all_rewards.append(X)\n",
        "    return all_rewards"
      ],
      "metadata": {
        "id": "sNLbACz1YTMS"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# c. Exp4"
      ],
      "metadata": {
        "id": "Lqo_duRWYWNd"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Policy\n",
        "def exp4_next_action(Q, E):\n",
        "    P = np.matmul(Q,E)\n",
        "    return np.random.choice(len(P),p=P), P\n",
        "\n",
        "# Expert weight update\n",
        "def update_importance_weighted_with_experts(Q,E,arm,reward,P,c):\n",
        "    X_hat = update_importance_weighted(np.zeros(E.shape[1]),arm,reward,P)\n",
        "    X_tilde = np.dot(E,X_hat)\n",
        "    Q = np.multiply(np.exp(c*X_tilde),Q)/np.sum(np.multiply(np.exp(c*X_tilde),Q))\n",
        "    return Q\n",
        "\n",
        "# Bandit interaction\n",
        "def Exp4(M,reward,horizon,c,advice):\n",
        "    all_rewards = []\n",
        "    Q = np.full(M,1/M)\n",
        "    for t in range(horizon):\n",
        "        E = advice(t)\n",
        "        A, P = exp4_next_action(Q,E)\n",
        "        X = reward(t,A)\n",
        "        if X is not None:\n",
        "            Q = update_importance_weighted_with_experts(Q,E,A,X,P,c)\n",
        "            all_rewards.append(X)\n",
        "    return all_rewards"
      ],
      "metadata": {
        "id": "t_rWuXcPYdbc"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "TViL1m6jKjRV"
      },
      "outputs": [],
      "source": [
        "ucb = UCB(k,reward,horizon)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "3b1Cw7Z0KjRV"
      },
      "outputs": [],
      "source": [
        "eta = np.sqrt(2*np.log(k)/(horizon*k))\n",
        "exp3 = Exp3(k,reward,horizon,eta)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "oqxeuzvXKjRV"
      },
      "outputs": [],
      "source": [
        "eta = np.sqrt(2*np.log(M)/(horizon*k))\n",
        "exp4 = Exp4(M*k,reward,horizon,eta,advice)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 319
        },
        "id": "6aWC5iINKjRW",
        "outputId": "0dd7f337-dc19-4f9a-e808-66f75347ca0e"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f3cd3772750>"
            ]
          },
          "metadata": {},
          "execution_count": 17
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "random = np.full(len(ucb),data['Liked'].value_counts(normalize=True)[1])\n",
        "\n",
        "fig1, ax1 = plt.subplots()\n",
        "ax1.plot(range(len(ucb)), np.cumsum(ucb), label='UCB')\n",
        "ax1.plot(range(len(exp3)), np.cumsum(exp3), label='Exp3')\n",
        "ax1.plot(range(len(exp4)), np.cumsum(exp4), label='Exp4')\n",
        "ax1.plot(range(len(random)), np.cumsum(random), label='Random')\n",
        "ax1.set_title(\"Cumulative reward using replay evaluation\")\n",
        "ax1.set_xlabel(\"Steps\")\n",
        "ax1.set_ylabel(\"Cumulative reward\")\n",
        "plt.legend()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "LtKaIP1wKjRW",
        "outputId": "109776f0-c0a0-43eb-e7fa-3612a7e49a3c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 319
        }
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f3cd43d6c90>"
            ]
          },
          "metadata": {},
          "execution_count": 18
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "cumulative_random = np.cumsum(random) / np.linspace(1, len(random), len(random))\n",
        "cumulative_ucb = np.cumsum(ucb) / np.linspace(1, len(ucb), len(ucb))\n",
        "cumulative_exp3 = np.cumsum(exp3) / np.linspace(1, len(exp3), len(exp3))\n",
        "cumulative_exp4 = np.cumsum(exp4) / np.linspace(1, len(exp4), len(exp4))\n",
        "\n",
        "fig1, ax1 = plt.subplots()\n",
        "ax1.plot(range(len(ucb)), np.asarray(pd.Series(cumulative_ucb).rolling(200).mean()), label='UCB')\n",
        "ax1.plot(range(len(exp3)), np.asarray(pd.Series(cumulative_exp3).rolling(200).mean()), label='Exp3')\n",
        "ax1.plot(range(len(exp4)), np.asarray(pd.Series(cumulative_exp4).rolling(200).mean()), label='Exp4')\n",
        "ax1.plot(range(len(random)), np.asarray(pd.Series(cumulative_random).rolling(200).mean()), label='Random')\n",
        "ax1.set_title(\"200-Round Rolling Mean Reward\")\n",
        "ax1.set_xlabel(\"Steps\")\n",
        "ax1.set_ylabel(\"Reward\")\n",
        "plt.legend()"
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "-SNODhZSZfpD"
      },
      "execution_count": null,
      "outputs": []
    }
  ],
  "metadata": {
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      "display_name": "Python 3.9.2 ('project-7Q2pLUeY-py3.9')",
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