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@enakai00
Last active May 15, 2019 00:03
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multi-armed bandits.ipynb
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "multi-armed bandits.ipynb",
"version": "0.3.2",
"provenance": [],
"collapsed_sections": [],
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/enakai00/dbfb695dd4602f4bc1edc8d0c98a85c5/multi-armed-bandits.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "code",
"metadata": {
"id": "-8IWbaVwQ211",
"colab_type": "code",
"colab": {}
},
"source": [
"import numpy as np\n",
"from numpy import random\n",
"from pandas import DataFrame"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "fQhRTF0kLS_B",
"colab_type": "code",
"colab": {}
},
"source": [
"class Bandit:\n",
" def __init__(self, arms=10):\n",
" self.arms = arms\n",
" self.means = random.normal(loc=0.0, scale=1.0, size=arms)\n",
" \n",
" def select(self, arm):\n",
" reward = random.normal(loc=self.means[arm], scale=1.0)\n",
" if arm == np.argmax(self.means):\n",
" optimal = 1\n",
" else:\n",
" optimal = 0\n",
" return reward, optimal\n",
" \n",
" def disturb(self):\n",
" self.means += random.normal(loc=0.0, scale=0.01, size=self.arms)"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "tzqbS8t4xOdK",
"colab_type": "text"
},
"source": [
"## Stationary problem"
]
},
{
"cell_type": "code",
"metadata": {
"id": "-wB7v8MCmq_B",
"colab_type": "code",
"colab": {}
},
"source": [
"def episode(bandit, epsilon, steps):\n",
"\n",
" def get_action(qs, epsilon):\n",
" if random.random() < epsilon: # explore\n",
" return random.randint(0, len(qs))\n",
" return np.argmax(qs)\n",
"\n",
"\n",
" rewards, optimals = [], []\n",
" qs = np.zeros(bandit.arms)\n",
" count = np.zeros(bandit.arms)\n",
" \n",
" for i in range(steps):\n",
" arm = get_action(qs, epsilon)\n",
" reward, optimal = bandit.select(arm)\n",
"\n",
" count[arm] += 1\n",
" qs[arm] += (reward - qs[arm]) / count[arm]\n",
" \n",
" rewards.append(reward)\n",
" optimals.append(optimal)\n",
" \n",
" return np.array(rewards), np.array(optimals)"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "4OthcvSRohXK",
"colab_type": "code",
"outputId": "d4512564-76dd-4e37-c22c-92d000b775a5",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 562
}
},
"source": [
"steps, trials = 1000, 2000\n",
"epsilons = [0, 0.01, 0.1]\n",
"\n",
"rewards_summary, optimals_summary = {}, {}\n",
"\n",
"for epsilon in epsilons:\n",
" avg_rewards, avg_optimals = 0, 0\n",
"\n",
" for trial in range(trials):\n",
" bandit = Bandit(arms=10)\n",
" rewards, optimals = episode(bandit, epsilon, steps)\n",
" avg_rewards += (rewards - avg_rewards) / (trial + 1)\n",
" avg_optimals += (optimals - avg_optimals) / (trial + 1)\n",
"\n",
" rewards_summary['ε={}'.format(epsilon)] = avg_rewards\n",
" optimals_summary['ε={}'.format(epsilon)] = avg_optimals\n",
"\n",
"DataFrame(rewards_summary).plot(title='Average reward')\n",
"DataFrame(optimals_summary).plot(title='% Optimal action')"
],
"execution_count": 4,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7fbf2d416438>"
]
},
"metadata": {
"tags": []
},
"execution_count": 4
},
{
"output_type": "display_data",
"data": {
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NFzY6bUvMSNQi1U7Gn3TarhdCS08tZfrB6Ybt+u8vP8kPIdAImG17oCKALkKIbEVRFubD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\nRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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N+1qBIfUYXHwPDHkevLysPv/VL8OAJ6BWQ6t8aOVI0+5UABCRYcBrWJPCv2eM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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "i14R4gw4x1rb",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 562
},
"outputId": "240e5f46-ead4-4d17-b7ad-8928ae85dd3b"
},
"source": [
"steps, trials = 1000, 2000\n",
"epsilons = [0.5, 0.1, 0.2, 1.0]\n",
"\n",
"rewards_summary, optimals_summary = {}, {}\n",
"\n",
"for epsilon in epsilons:\n",
" avg_rewards, avg_optimals = 0, 0\n",
"\n",
" for trial in range(trials):\n",
" bandit = Bandit(arms=10)\n",
" rewards, optimals = episode(bandit, epsilon, steps)\n",
" avg_rewards += (rewards - avg_rewards) / (trial + 1)\n",
" avg_optimals += (optimals - avg_optimals) / (trial + 1)\n",
"\n",
" rewards_summary['ε={}'.format(epsilon)] = avg_rewards\n",
" optimals_summary['ε={}'.format(epsilon)] = avg_optimals\n",
"\n",
"DataFrame(rewards_summary).plot(title='Average reward')\n",
"DataFrame(optimals_summary).plot(title='% Optimal action')"
],
"execution_count": 6,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7fbf2aaa0cc0>"
]
},
"metadata": {
"tags": []
},
"execution_count": 6
},
{
"output_type": "display_data",
"data": {
"image/png": 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+7CBT3wIdqlWmfTXjvN4BViGQo9H+k3qONiyr8vr613l3zze2/Rae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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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O23eYcXAGA2sN5KcTPxnTh9Ydym+nTcHN6nnXo6pHVdoGtmV37G6rekY1GcW3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\nAKCUUh2UBgCllOqg/h+kV5Q1IS/rHgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "2y-XitMBxg54",
"colab_type": "text"
},
"source": [
"## Nonstationary problem"
]
},
{
"cell_type": "code",
"metadata": {
"id": "CoEEVKoxz0Z3",
"colab_type": "code",
"colab": {}
},
"source": [
"def episode(bandit, epsilon, steps):\n",
"\n",
" def get_action(qs, epsilon):\n",
" if random.random() < epsilon: # explore\n",
" return random.randint(0, len(qs))\n",
" return np.argmax(qs)\n",
"\n",
"\n",
" rewards, optimals = [], []\n",
" qs = np.zeros(bandit.arms)\n",
" count = np.zeros(bandit.arms)\n",
" \n",
" for i in range(steps):\n",
" arm = get_action(qs, epsilon)\n",
" reward, optimal = bandit.select(arm)\n",
"\n",
" count[arm] += 1\n",
" qs[arm] += (reward - qs[arm]) / count[arm]\n",
" \n",
" rewards.append(reward)\n",
" optimals.append(optimal)\n",
" bandit.disturb() # nonstationary\n",
" \n",
" return np.array(rewards), np.array(optimals)"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "Jd3mvFtnz7ON",
"colab_type": "code",
"outputId": "e6bad7e4-c7d1-44c6-837f-064a06cdfe4e",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 562
}
},
"source": [
"steps, trials = 1000, 2000\n",
"epsilons = [0, 0.01, 0.1]\n",
"\n",
"rewards_summary, optimals_summary = {}, {}\n",
"\n",
"for epsilon in epsilons:\n",
" avg_rewards, avg_optimals = 0, 0\n",
"\n",
" for trial in range(trials):\n",
" bandit = Bandit(arms=10)\n",
" rewards, optimals = episode(bandit, epsilon, steps)\n",
" avg_rewards += (rewards - avg_rewards) / (trial + 1)\n",
" avg_optimals += (optimals - avg_optimals) / (trial + 1)\n",
"\n",
" rewards_summary['ε={}'.format(epsilon)] = avg_rewards\n",
" optimals_summary['ε={}'.format(epsilon)] = avg_optimals\n",
"\n",
"DataFrame(rewards_summary).plot(title='Average reward')\n",
"DataFrame(optimals_summary).plot(title='% Optimal action')"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7ff12e9cc320>"
]
},
"metadata": {
"tags": []
},
"execution_count": 6
},
{
"output_type": "display_data",
"data": {
"image/png": 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MATh0RrYPak+/6tb6Lk9UfoL+1ftb7lNFWyqheuHqhA4OpUJABd25ulXsRpty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\nj7KS4qAAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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UWAY4A99rrQ8qpaYBO7TWC/LLblRKHQLMwL+01gkVGXhVlZCVwGd7PmPe0XnW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\nzjmXQv8DkL2vewnSkb0AAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "RPdkthQo1qm1",
"colab_type": "code",
"outputId": "5966c35a-686a-4994-9f40-ea61f6f1c090",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 562
}
},
"source": [
"def episode(bandit, epsilon, steps):\n",
" \n",
" def get_action(qs, epsilon):\n",
" if random.random() < epsilon: # explore\n",
" return random.randint(0, len(qs))\n",
" return np.argmax(qs)\n",
"\n",
"\n",
" rewards, optimals = [], []\n",
" qs = np.zeros(bandit.arms)\n",
" \n",
" for i in range(steps):\n",
" arm = get_action(qs, epsilon)\n",
" reward, optimal = bandit.select(arm)\n",
"\n",
" qs[arm] += (reward - qs[arm]) * 0.1\n",
" \n",
" rewards.append(reward)\n",
" optimals.append(optimal)\n",
" bandit.disturb()\n",
" \n",
" return np.array(rewards), np.array(optimals)\n",
"\n",
"\n",
"steps, trials = 10000, 2000\n",
"epsilons = [0.1]\n",
"\n",
"rewards_summary, optimals_summary = {}, {}\n",
"\n",
"for epsilon in epsilons:\n",
" avg_rewards, avg_optimals = 0, 0\n",
"\n",
" for trial in range(trials):\n",
" bandit = Bandit(arms=10)\n",
" rewards, optimals = episode(bandit, epsilon, steps)\n",
" avg_rewards += (rewards - avg_rewards) / (trial + 1)\n",
" avg_optimals += (optimals - avg_optimals) / (trial + 1)\n",
"\n",
" rewards_summary['ε={}'.format(epsilon)] = avg_rewards\n",
" optimals_summary['ε={}'.format(epsilon)] = avg_optimals\n",
"\n",
"DataFrame(rewards_summary).plot(title='Average reward')\n",
"DataFrame(optimals_summary).plot(title='% Optimal action')"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7ff12e8bef28>"
]
},
"metadata": {
"tags": []
},
"execution_count": 7
},
{
"output_type": "display_data",
"data": {
"image/png": 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mrvdWlkivER3FioeG0uPhOVzQoRFv33J+wba4mGjSHkuxeVmNqcYCBn4ReRcY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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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iIomRcsk9cqAwgIz0lDtEEZGoUi7zbdtdWGbezBIUiYhI4qRcco/sJfPMT9RL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\naQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "heLvOczrH2sR",
"colab_type": "text"
},
"source": [
"## UCB"
]
},
{
"cell_type": "code",
"metadata": {
"id": "QKhHjOP5CLDb",
"colab_type": "code",
"colab": {}
},
"source": [
"def episode(bandit, epsilon, steps):\n",
"\n",
" def get_action(qs, epsilon):\n",
" if random.random() < epsilon: # explore\n",
" return random.randint(0, len(qs))\n",
" return np.argmax(qs)\n",
" \n",
" rewards, optimals = [], []\n",
" qs = np.zeros(bandit.arms)\n",
" count = np.zeros(bandit.arms)\n",
" \n",
" for i in range(steps):\n",
" arm = get_action(qs, epsilon)\n",
" reward, optimal = bandit.select(arm)\n",
"\n",
" count[arm] += 1\n",
" qs[arm] += (reward - qs[arm]) / count[arm]\n",
" \n",
" rewards.append(reward)\n",
" optimals.append(optimal)\n",
" \n",
" return np.array(rewards), np.array(optimals)\n",
"\n",
"\n",
"def episode_ucb(bandit, steps):\n",
"\n",
" def get_ucb_action(qs, t, count):\n",
" ucb_qs = [qs[arm]+2*np.sqrt(np.log(t+1)/(count[arm]+1))\n",
" for arm in range(len(count))]\n",
" return np.argmax(ucb_qs)\n",
"\n",
"\n",
" rewards, optimals = [], []\n",
" qs = np.zeros(bandit.arms)\n",
" count = np.zeros(bandit.arms)\n",
"\n",
" for i in range(steps):\n",
" arm = get_ucb_action(qs, i, count)\n",
" reward, optimal = bandit.select(arm)\n",
"\n",
" count[arm] += 1\n",
" qs[arm] += (reward - qs[arm]) / count[arm]\n",
" \n",
" rewards.append(reward)\n",
" optimals.append(optimal)\n",
" \n",
" return np.array(rewards), np.array(optimals)"
],
"execution_count": 0,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "DjbMHDC5I1fo",
"colab_type": "code",
"outputId": "1f038b14-ca8c-41d6-90a4-0c19c3b3d16f",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 562
}
},
"source": [
"steps, trials = 1000, 2000\n",
"\n",
"rewards_summary, optimals_summary = {}, {}\n",
"\n",
"# epsilon-gredy\n",
"avg_rewards, avg_optimals = 0, 0\n",
"\n",
"for trial in range(trials):\n",
" bandit = Bandit(arms=10)\n",
" rewards, optimals = episode(bandit, epsilon, steps)\n",
" avg_rewards += (rewards - avg_rewards) / (trial + 1)\n",
" avg_optimals += (optimals - avg_optimals) / (trial + 1)\n",
"\n",
"rewards_summary['ε-greedy'] = avg_rewards\n",
"optimals_summary['ε-greedy'] = avg_optimals\n",
"\n",
"# UCB\n",
"avg_rewards, avg_optimals = 0, 0\n",
"\n",
"for trial in range(trials):\n",
" bandit = Bandit(arms=10)\n",
" rewards, optimals = episode_ucb(bandit, steps)\n",
" avg_rewards += (rewards - avg_rewards) / (trial + 1)\n",
" avg_optimals += (optimals - avg_optimals) / (trial + 1)\n",
"\n",
"rewards_summary['ucb'] = avg_rewards\n",
"optimals_summary['ucb'] = avg_optimals\n",
" \n",
"DataFrame(rewards_summary).plot(title='Average reward')\n",
"DataFrame(optimals_summary).plot(title='% Optimal action')"
],
"execution_count": 0,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x7ff12e6faac8>"
]
},
"metadata": {
"tags": []
},
"execution_count": 10
},
{
"output_type": "display_data",
"data": {
"image/png": 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l5hpHdsNLaTDjjQCds91tc2zx8svHwOofPPtTnnSH5qXuX8inccNtTUTB3jXw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\ncy5CXtydcy5CXtydcy5CXtydcy5C/wCwyss4kmkapQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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mA/MBP+AdY8xGEZkOrDLGzAH+CbwpIvdgH65eX1Zg93bTpk1jwYIFZGZmMnLk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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": []
}
}
]
}
]
}
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