kiwamizamurai/linucb-lints.ipynb

## linucb-lints.ipynb
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        "4067c363f0c54c55abf9dab554d58fc6": {
          "model_module": "@jupyter-widgets/controls",
          "model_name": "DescriptionStyleModel",
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            "_view_name": "StyleView",
            "_model_name": "DescriptionStyleModel",
            "description_width": "",
            "_view_module": "@jupyter-widgets/base",
            "_model_module_version": "1.5.0",
            "_view_count": null,
            "_view_module_version": "1.2.0",
            "_model_module": "@jupyter-widgets/controls"
          }
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        "b7665f709db04220829c8b2a9518b5df": {
          "model_module": "@jupyter-widgets/base",
          "model_name": "LayoutModel",
          "state": {
            "_view_name": "LayoutView",
            "grid_template_rows": null,
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            "justify_content": null,
            "_view_module": "@jupyter-widgets/base",
            "overflow": null,
            "_model_module_version": "1.2.0",
            "_view_count": null,
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            "_model_module": "@jupyter-widgets/base",
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        }
      }
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/kiwamizamurai/755bb64881f074e1b32b74df7f071615/linucb-lints.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lsaTEbrtgFkT",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "from sklearn.linear_model import LogisticRegression\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "plt.rcParams[\"figure.figsize\"] = (22, 9)\n",
        "plt.rcParams[\"font.size\"] = 25\n",
        "import seaborn as sns\n",
        "sns.set()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-llTJAD_g-Vb",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "f6c504b7-5f03-4bdb-cfdc-62df4185f923"
      },
      "source": [
        "np.random.seed(7)\n",
        "\n",
        "n = 10000  # number of data\n",
        "d = 10   # number of features\n",
        "K = 5  # number of actions\n",
        "\n",
        "X = np.random.random((n, d))\n",
        "theta = np.random.normal(0, 1, (K, d)) # true\n",
        "# will fail unless normal gauss,\n",
        "\n",
        "print(X.shape)\n",
        "print(theta.shape)"
      ],
      "execution_count": 262,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(10000, 10)\n",
            "(5, 10)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PQLrK6jpiX7P",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "c6470afe-cd77-4dd2-b159-d3be1771def1"
      },
      "source": [
        "y = np.dot(X, theta.T)\n",
        "print(y.shape)"
      ],
      "execution_count": 263,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(10000, 5)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dcep9ORhjUg4",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "2292495b-4d05-4d21-9850-3bf38b321a16"
      },
      "source": [
        "optimal_a = np.array(y.argmax(axis=1), dtype=int)\n",
        "\n",
        "optimal_a"
      ],
      "execution_count": 265,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1, 3, 3, ..., 1, 3, 3])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 265
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EqJhtG4Djmi4",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 556
        },
        "outputId": "70faefcc-3841-4b69-937a-0c24aeea5598"
      },
      "source": [
        "plt.title(\"Distribution of Best Arm choices\")\n",
        "plt.hist(optimal_a, bins=range(0, K+1));"
      ],
      "execution_count": 266,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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PzJo1K295y1sqPRYU7aKLLsptt92Wp556KnvuuWcGDRqUW265pdJj\nQfF+//vfZ9y4cdl3332z2267JUn23nvvzJ07t8KTQdmeeuqpfOITn8izzz6bqqqqDBw4MF/4whfy\njne8o9KjQY/S0z95FHalxx///9q3oxqAYRiGgkERAsVXBmE7HK3GYpOsOwT+fpKf2nvXOafuvbXW\nqpmp7v572mfEPwAAAAAI5fYLAAAAAKHEPwAAAAAIJf4BAAAAQCjxDwAAAABCiX8AAAAAEEr8AwAA\nAIBQ4h8AAAAAhBL/AAAAACDUC5NYcG4/HP7DAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 1584x648 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kz9biwOmla45",
        "colab_type": "text"
      },
      "source": [
        "## LinUCB (disjoint model)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "y0Lm4HhEkGL6",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "choices = np.zeros(n)\n",
        "rewards = np.zeros(n)\n",
        "\n",
        "b = np.zeros_like(theta)\n",
        "A = np.zeros((K, d, d)) # tensor due to K arms\n",
        "\n",
        "for a in range (0, K):\n",
        "    A[a] = np.identity(d)\n",
        "\n",
        "th_hat = np.zeros_like(theta)\n",
        "p = np.zeros(K)\n",
        "alph = 0.2"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "G-GlMm6Yr2md",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "30f3dfb6-c33b-494e-b93e-859b5418a5cc"
      },
      "source": [
        "from tqdm import tqdm_notebook as tqdm\n",
        "!jupyter nbextension enable --py --sys-prefix widgetsnbextension"
      ],
      "execution_count": 268,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Enabling notebook extension jupyter-js-widgets/extension...\n",
            "      - Validating: \u001b[32mOK\u001b[0m\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0YxwDeQOkjQl",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 118,
          "referenced_widgets": [
            "512a4aca868e4af1891d717ba30c837d",
            "0278509dc6344f2c9472794a332cf75a",
            "4fb3dbc8246143c698c323b0a852901d",
            "ad99f751b48b4334a8be293d91dc802f",
            "b7ad268493e34a30b2bcbc4f41402546",
            "238edebeade6448bb166388513607ceb",
            "48af0e74106843edac4498865e9d1f2f",
            "4bb1d45f466a4a62ad882dfb16b7479f"
          ]
        },
        "outputId": "210ec8f3-7606-4749-e478-50ad0ebb8449"
      },
      "source": [
        "for i in tqdm(range(0, n)):\n",
        "  x_i = X[i]   # the current context vector\n",
        "  for a in range (0, K):\n",
        "    A_inv = np.linalg.inv(A[a])     # corresponding covariance matrix\n",
        "    th_hat[a] = A_inv.dot(b[a])\n",
        "\n",
        "    ta = x_i.dot(A_inv).dot(x_i)\n",
        "    upperbound = alph * np.sqrt(ta) # upper part of variance interval\n",
        "\n",
        "    linear_model = th_hat[a].dot(x_i)\n",
        "    p[a] = linear_model + upperbound\n",
        "\n",
        "  norms[i] = np.linalg.norm(th_hat - theta,'fro')    # validate LinUCB\n",
        "  choices[i] = np.argmax(p)\n",
        "\n",
        "  rewards[i] = theta[int(choices[i])].dot(x_i)  # using actual theta to figure out reward\n",
        "\n",
        "  A[int(choices[i])] += np.outer(x_i,x_i)\n",
        "  b[int(choices[i])] += rewards[i] * x_i"
      ],
      "execution_count": 269,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:1: TqdmDeprecationWarning: This function will be removed in tqdm==5.0.0\n",
            "Please use `tqdm.notebook.tqdm` instead of `tqdm.tqdm_notebook`\n",
            "  \"\"\"Entry point for launching an IPython kernel.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "512a4aca868e4af1891d717ba30c837d",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(IntProgress(value=0, max=10000), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Opoxnz54ERrj",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 557
        },
        "outputId": "32c0c1df-c94d-41ab-8f5d-5bb05b964ac6"
      },
      "source": [
        "sns.countplot(choices)"
      ],
      "execution_count": 271,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f0766542c88>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 271
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 1584x648 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mxpwpC3CsihD",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 573
        },
        "outputId": "f0b003db-f989-4a56-c432-fe90179a3481"
      },
      "source": [
        "plt.subplot(121)\n",
        "plt.plot(norms);\n",
        "plt.title(\"Frobenius norm of estimated theta vs actual\")\n",
        "\n",
        "plt.subplot(122)\n",
        "regret = (y.max(axis=1) - rewards)\n",
        "\n",
        "plt.plot(regret.cumsum())\n",
        "plt.title(\"Cumulative Regret\")"
      ],
      "execution_count": 272,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Cumulative Regret')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 272
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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dfvrpR73P5MmTdeWVV550Uc3FMOihBwAAANjBv7buk980FRkWYnUp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\nAj1kJcs0FbBMbdrRoO89uVkb3qvzuiQAAJAhXNdN7HLLphgAACBFCPS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aa69pyZIlWrx4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\nAAAAkEb+f6toKS1hfQrEAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 1584x648 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UigqcQ0TuoCX",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "class LinUCB():\n",
        "  def __init__(self, n, K, d, alpha=0.2):\n",
        "    self.choices = np.zeros(n)\n",
        "    self.rewards = np.zeros(n)\n",
        "    self.norms = np.zeros(n)\n",
        "    self.K = K\n",
        "\n",
        "    self.b = np.zeros((self.K, d))\n",
        "    self.A = np.zeros((self.K, d, d)) # tensor due to K arms\n",
        "\n",
        "    for a in range (0, self.K):\n",
        "      self.A[a] = np.identity(d)\n",
        "\n",
        "    self.th_hat = np.zeros((self.K, d))\n",
        "    self.p = np.zeros(self.K)\n",
        "    self.alpha = alpha\n",
        "\n",
        "  def select_arm(self, i, x_i):\n",
        "    for a in range (0, self.K):\n",
        "      A_inv = np.linalg.inv(self.A[a])     # corresponding covariance matrix\n",
        "      self.th_hat[a] = A_inv.dot(self.b[a])\n",
        "\n",
        "      ta = x_i.dot(A_inv).dot(x_i)\n",
        "      upperbound = self.alpha * np.sqrt(ta) # upper part of variance interval\n",
        "\n",
        "      linear_model = self.th_hat[a].dot(x_i)\n",
        "      self.p[a] = linear_model + upperbound\n",
        "\n",
        "    self.norms[i] = np.linalg.norm(self.th_hat - theta, 'fro')    # validate LinUCB\n",
        "    self.choices[i] = np.argmax(self.p)\n",
        "    self.rewards[i] = theta[int(self.choices[i])].dot(x_i)  # using actual theta to figure out reward\n",
        "\n",
        "  def update(self, i, x_i, r):\n",
        "    # self.rewards[i] = self.th_hat[int(np.argmax(self.p))].dot(x_i)\n",
        "\n",
        "    self.A[int(self.choices[i])] += np.outer(x_i, x_i)\n",
        "    self.b[int(choices[i])] += r * x_i\n",
        "    # self.b[int(self.choices[i])] += self.rewards[i] * x_i"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "S6d5DJkwkjbu",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 118,
          "referenced_widgets": [
            "68b757092b9846d39c87e8e96f9f95df",
            "461df47bcac5417f9ea6be1e8dba7174",
            "57d0454aef7844cb91fc82617c60203d",
            "41535a6922244ceab762c15088981729",
            "0dd13905ecc44def8f88afee018a369c",
            "db08f35ed4bf40d28de6055443e532dc",
            "7630b179449c462bbaba2dd0afb752fd",
            "17fbbd06f4b448e2b15d03f243c590ad"
          ]
        },
        "outputId": "1f435130-8503-48c1-9681-acb293c1fc77"
      },
      "source": [
        "LinUCB_3 = LinUCB(X.shape[0], K, X.shape[1], alpha=0.2)\n",
        "LinUCB_5 = LinUCB(X.shape[0], K, X.shape[1], alpha=0.6)\n",
        "LinUCB_7 = LinUCB(X.shape[0], K, X.shape[1], alpha=1.0)\n",
        "\n",
        "eps_rewards = []\n",
        "\n",
        "for i in tqdm(range(0, n)):\n",
        "  LinUCB_3.select_arm(i, X[i])\n",
        "  chosen_arm_3 = int(np.argmax(LinUCB_3.p))\n",
        "  r_3 = y[i, chosen_arm_3]\n",
        "\n",
        "  LinUCB_5.select_arm(i, X[i])\n",
        "  chosen_arm_5 = int(np.argmax(LinUCB_5.p))\n",
        "  r_5 = y[i, chosen_arm_5]\n",
        "\n",
        "  LinUCB_7.select_arm(i, X[i])\n",
        "  chosen_arm_7 = int(np.argmax(LinUCB_7.p))\n",
        "  r_7 = y[i, chosen_arm_7]\n",
        "\n",
        "  LinUCB_3.update(i, X[i], r_3)\n",
        "  LinUCB_5.update(i, X[i], r_5)\n",
        "  LinUCB_7.update(i, X[i], r_7)\n",
        "\n",
        "  eps_rewards.append(y[i, np.random.randint(0, K)])"
      ],
      "execution_count": 297,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:7: TqdmDeprecationWarning: This function will be removed in tqdm==5.0.0\n",
            "Please use `tqdm.notebook.tqdm` instead of `tqdm.tqdm_notebook`\n",
            "  import sys\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "68b757092b9846d39c87e8e96f9f95df",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(IntProgress(value=0, max=10000), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UsgJr26P6Im-",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 557
        },
        "outputId": "2e3e36ff-7c3e-4d0c-a5bb-0990b6e44075"
      },
      "source": [
        "plt.plot(LinUCB_3.norms, label='alpha = 0.2')\n",
        "plt.plot(LinUCB_5.norms, label='alpha = 0.6')\n",
        "plt.plot(LinUCB_7.norms, label='alpha = 1.0')\n",
        "plt.legend(frameon=False, loc=0, ncol=1, prop={'size': 20})"
      ],
      "execution_count": 298,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f07646b7320>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 298
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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mHc4uAwAAAACARnegIF3BnoEK9gyq1l5hr9TTG35frS3Mu51u7XAT4R6aDAI+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\nAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 1584x648 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Crh6Zsbs03E4",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 573
        },
        "outputId": "f624b6a2-2e15-444f-d102-52b79d93e501"
      },
      "source": [
        "regret_3 = (y.max(axis=1) - LinUCB_3.rewards)\n",
        "plt.plot(regret_3.cumsum(), label='alpha = 0.2')\n",
        "regret_5 = (y.max(axis=1) - LinUCB_5.rewards)\n",
        "plt.plot(regret_5.cumsum(), label='alpha = 0.6')\n",
        "regret_7 = (y.max(axis=1) - LinUCB_7.rewards)\n",
        "plt.plot(regret_7.cumsum(), label='alpha = 1.0')\n",
        "regret_eg = y.max(axis=1) - np.array(eps_rewards)\n",
        "plt.plot(regret_eg.cumsum(), label='EpsilonG')\n",
        "\n",
        "plt.title(\"Cumulative Regret\")\n",
        "plt.legend(frameon=False, loc=0, ncol=1, prop={'size': 20})"
      ],
      "execution_count": 300,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f0764584048>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 300
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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TF7eb2Nhd3Hvv/dUaq0WLljz00MMV2gYMGISfXwCJifEkJSXg7x9YoX/s2EcqhIIADzzw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\nH161C5PDqg2nAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 1584x648 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AojDnPTEMTVK",
        "colab_type": "text"
      },
      "source": [
        "## LinTS"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "88kK7F5e17N_",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "class LinTS():\n",
        "  def __init__(self, n, K, d, v=0.2):\n",
        "    self.choices = np.zeros(n)\n",
        "    self.rewards = np.zeros(n)\n",
        "    self.norms = np.zeros(n)\n",
        "    self.K = K\n",
        "    self.v = v\n",
        "\n",
        "    self.B = np.zeros((self.K, d, d)) # tensor due to K arms\n",
        "    self.mu = np.zeros((K, d))\n",
        "    self.f = np.zeros((K, d))\n",
        "\n",
        "    for a in range (0, self.K):\n",
        "      self.B[a] = np.identity(d)\n",
        "\n",
        "    self.th_hat = np.zeros((self.K, d))\n",
        "    self.p = np.zeros(self.K)\n",
        "\n",
        "  def select_arm(self, i, x_i):\n",
        "    for a in range (0, self.K):\n",
        "      mu_tilda = np.random.multivariate_normal(self.mu[a], (self.v**2)*np.linalg.inv(self.B[a]), 1)\n",
        "      self.p[a] = np.dot(mu_tilda, x_i)\n",
        "\n",
        "    self.norms[i] = np.linalg.norm(self.th_hat - theta, 'fro')    # validate LinTS\n",
        "    self.choices[i] = np.argmax(self.p)\n",
        "    self.rewards[i] = theta[int(self.choices[i])].dot(x_i)  # using actual theta to figure out reward\n",
        "\n",
        "  def update(self, i, x_i, r):\n",
        "\n",
        "    self.B[int(self.choices[i])] += np.outer(x_i, x_i)\n",
        "    self.f[int(choices[i])] += r * x_i\n",
        "    self.mu[int(choices[i])] += np.dot(np.linalg.inv(self.B[int(self.choices[i])]),  self.f[int(choices[i])])\n",
        "    # self.b[int(self.choices[i])] += self.rewards[i] * x_i"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GyE4o_Y4LLF-",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 118,
          "referenced_widgets": [
            "78ca8a7864c14fee8bce228098612807",
            "632c2d3e920a41858adacf9fbee23e55",
            "614d00533d8c401294e7cc46282c4128",
            "f50876c0a8ba47f3917903a99f50e4a4",
            "505629254709434ea2a82910c241fcee",
            "29a183a6b0d34cf18f543d8edfdebaaf",
            "4067c363f0c54c55abf9dab554d58fc6",
            "b7665f709db04220829c8b2a9518b5df"
          ]
        },
        "outputId": "a99124ac-0e80-4c39-f79c-2b138e185c22"
      },
      "source": [
        "LinTS_2 = LinTS(X.shape[0], K, X.shape[1], v=0.2)\n",
        "LinTS_6 = LinTS(X.shape[0], K, X.shape[1], v=0.6)\n",
        "\n",
        "eps_rewards = []\n",
        "\n",
        "for i in tqdm(range(0, n)):\n",
        "  LinTS_2.select_arm(i, X[i])\n",
        "  chosen_arm_2 = int(np.argmax(LinTS_2.p))\n",
        "  r_2 = y[i, chosen_arm_2]\n",
        "\n",
        "  LinTS_6.select_arm(i, X[i])\n",
        "  chosen_arm_6 = int(np.argmax(LinTS_6.p))\n",
        "  r_6 = y[i, chosen_arm_6]\n",
        "\n",
        "  LinTS_2.update(i, X[i], r_2)\n",
        "  LinTS_6.update(i, X[i], r_6)\n",
        "\n",
        "  eps_rewards.append(y[i, np.random.randint(0, K)])"
      ],
      "execution_count": 332,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:6: TqdmDeprecationWarning: This function will be removed in tqdm==5.0.0\n",
            "Please use `tqdm.notebook.tqdm` instead of `tqdm.tqdm_notebook`\n",
            "  \n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "78ca8a7864c14fee8bce228098612807",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "HBox(children=(IntProgress(value=0, max=10000), HTML(value='')))"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mf6xkMioZlJl",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 557
        },
        "outputId": "0ceeae93-c822-419b-e352-a510649a8daa"
      },
      "source": [
        "plt.plot(LinTS_2.norms, label='v = 0.2')\n",
        "plt.plot(LinTS_6.norms, label='v = 0.6')\n",
        "plt.legend(frameon=False, loc=0, ncol=1, prop={'size': 20})"
      ],
      "execution_count": 333,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f0764511780>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 333
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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+fJYuXZo99thj/bEhQ4ako6MjK1as2OJjgwYN2qafB7Z33/jGN3Li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\n",
            "text/plain": [
              "<Figure size 1584x648 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pA_cJFUNbBH0",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 573
        },
        "outputId": "9f88ddd7-dafd-49bd-96a3-a913d53098e8"
      },
      "source": [
        "regret_2 = (y.max(axis=1) - LinTS_2.rewards)\n",
        "plt.plot(regret_2.cumsum(), label='v = 0.2')\n",
        "regret_6 = (y.max(axis=1) - LinTS_6.rewards)\n",
        "plt.plot(regret_6.cumsum(), label='v = 0.6')\n",
        "\n",
        "regret_eg = y.max(axis=1) - np.array(eps_rewards)\n",
        "plt.plot(regret_eg.cumsum(), label='EpsilonG')\n",
        "\n",
        "plt.title(\"Cumulative Regret\")\n",
        "plt.legend(frameon=False, loc=0, ncol=1, prop={'size': 20})"
      ],
      "execution_count": 336,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f07642fa080>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 336
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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rr2r06NGSpM2bN+vVV1+VxWLR+PHj9ctf/lIeHh5X1QYAAAAAAHA1isobtS23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            "text/plain": [
              "<Figure size 1584x648 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ABTjJuEacAco",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 573
        },
        "outputId": "34479701-3d74-4903-a41b-afa63fbbe41f"
      },
      "source": [
        "regret_3 = (y.max(axis=1) - LinUCB_3.rewards)\n",
        "plt.plot(regret_3.cumsum(), label='LinUCB alpha = 0.2', marker='.')\n",
        "regret_5 = (y.max(axis=1) - LinUCB_5.rewards)\n",
        "plt.plot(regret_5.cumsum(), label='LinUCB alpha = 0.6', marker='.')\n",
        "\n",
        "regret_2 = (y.max(axis=1) - LinTS_2.rewards)\n",
        "plt.plot(regret_2.cumsum(), label='LinTS v = 0.2')\n",
        "regret_6 = (y.max(axis=1) - LinTS_6.rewards)\n",
        "plt.plot(regret_6.cumsum(), label='LinTS v = 0.6')\n",
        "\n",
        "regret_eg = y.max(axis=1) - np.array(eps_rewards)\n",
        "plt.plot(regret_eg.cumsum(), label='EpsilonG', ls='--')\n",
        "\n",
        "plt.title(\"Cumulative Regret\")\n",
        "plt.legend(frameon=False, loc=0, ncol=1, prop={'size': 20})"
      ],
      "execution_count": 342,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f0763ff7518>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 342
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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RuesZTUZ2n93Hb2c2c/TCceyt7ejqFcw9jcJoULO+pcsTC9M/FYvZmjb1tnQJ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\n6eX2fXp/4EM5lqNrajbolqU3q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            "text/plain": [
              "<Figure size 1584x648 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ChoMiNGndguq",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 557
        },
        "outputId": "ea5be78d-75f1-4ed4-93c5-50ceaa22df25"
      },
      "source": [
        "sns.countplot(LinUCB_3.choices)"
      ],
      "execution_count": 343,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f076435f4a8>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 343
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 1584x648 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qQQpdIktcMep",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 557
        },
        "outputId": "eb2beaf4-cfe0-4748-b61b-52784a580fa6"
      },
      "source": [
        "sns.countplot(LinTS_6.choices)"
      ],
      "execution_count": 344,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f0763f72b38>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 344
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 1584x648 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "h6cXmAXrdmgq",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 557
        },
        "outputId": "ab928ccb-24db-469d-b5a4-36f1991bf5bc"
      },
      "source": [
        "sns.countplot(LinUCB_5.choices)"
      ],
      "execution_count": 345,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f0763ed8128>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 345
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 1584x648 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "r2mhl8Qrdrse",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 557
        },
        "outputId": "e1df579b-f38d-420d-9f36-e699986c216b"
      },
      "source": [
        "sns.countplot(LinTS_2.choices)"
      ],
      "execution_count": 346,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f0763e52470>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 346
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 1584x648 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yMs4eyeodvsK",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}