{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 7章 線形モデル上のバンディット 報酬が2値の場合\n", "\n", "Author: hagino3000 \n", "Date: 2016-11-30\n", "\n", "「バンディット問題の理論とアルゴリズム」[1] の7章のアルゴリズムを実装して動かしてみる． \n", "報酬が二値のケース\n", "\n", "- LinUCB\n", "- 線形モデル上のトンプソン抽出\n", "- ロジスティック回帰モデル上のトンプソン抽出\n", "\n", "\n", "[1] 「バンディット問題の理論とアルゴリズム」本多淳也／中村篤祥・著 http://www.kspub.co.jp/book/detail/1529175.html" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 実験データ\n", "\n", "報酬はネット広告のクリック = {0, 1} ，μは2%前後 とする \n", "デザインとフォントは時刻tのコンテキスト(オーディエンス属性)に依存する，コンテキスト付きバンディット問題" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# 報酬は {0, 1}\n", "# 真の報酬モデル\n", "campaigns = {\n", " 'campaign_a': 0.1,\n", " 'campaign_b': 0.25,\n", " 'campaign_c': 0.4,\n", " 'campaign_d': 0.3,\n", " 'campaign_e': 0.2,\n", " 'campaign_f': 0.1\n", "}\n", "attribute = {\n", " 'men_20': -4,\n", " 'men_30': -3.8,\n", " 'female_20': -4,\n", " 'female_30': -3.8 \n", "}\n", "# デザインとfontはユーザー属性に依存して報酬が決まる\n", "contextual_attrs = {\n", " 'men_20': {\n", " 'design': {\n", " 'a': 0.2,\n", " 'b':-0.1,\n", " 'c': 0.1,\n", " 'd': 0.01\n", " },\n", " 'font': {'a': 0.1, 'b': 0.2}\n", " },\n", " 'men_30': {\n", " 'design': {\n", " 'a': 0.3,\n", " 'b':-0.1,\n", " 'c': 0.15,\n", " 'd': 0.01\n", " },\n", " 'font': {'a': 0.1, 'b': -0.1}\n", " },\n", " 'female_20': {\n", " 'design': {\n", " 'a':-0.10,\n", " 'b': 0.20, \n", " 'c': 0.1,\n", " 'd': 0.01\n", " },\n", " 'font': {'a': 0.1,'b': -0.1}\n", " }, \n", " 'female_30': {\n", " 'design': {\n", " 'a':-0.1,\n", " 'b': 0.2, \n", " 'c': 0.12,\n", " 'd': 0.01\n", " },\n", " 'font': {'a': -0.1, 'b': 0.1}\n", " }\n", "}\n", "\n", "contextual_columns = []\n", "contextual_values = []\n", "for attr, attr_v in contextual_attrs.items():\n", " for el, el_v in attr_v.items():\n", " for type_name, value in el_v.items():\n", " contextual_columns.append(attr + '_' + el + '_' + type_name)\n", " contextual_values.append(value)\n", "\n", "actions = []\n", "for a in [campaigns.keys(), attribute.keys(), contextual_columns]:\n", " actions.extend(a)\n", "theta = []\n", "for a in [campaigns.values(), attribute.values(), contextual_values]:\n", " theta.extend(a)\n", "theta = np.array(theta)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "['campaign_e', 'campaign_d', 'campaign_a', 'campaign_c', 'campaign_b', 'campaign_f', 'men_20', 'female_30', 'men_30', 'female_20', 'men_20_font_b', 'men_20_font_a', 'men_20_design_b', 'men_20_design_d', 'men_20_design_a', 'men_20_design_c', 'female_30_font_b', 'female_30_font_a', 'female_30_design_b', 'female_30_design_d', 'female_30_design_a', 'female_30_design_c', 'men_30_font_b', 'men_30_font_a', 'men_30_design_b', 'men_30_design_d', 'men_30_design_a', 'men_30_design_c', 'female_20_font_b', 'female_20_font_a', 'female_20_design_b', 'female_20_design_d', 'female_20_design_a', 'female_20_design_c']\n" ] } ], "source": [ "# actionの要素\n", "print(actions)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0.2 0.3 0.1 0.4 0.25 0.1 -4. -3.8 -3.8 -4. 0.2 0.1\n", " -0.1 0.01 0.2 0.1 0.1 -0.1 0.2 0.01 -0.1 0.12 -0.1 0.1\n", " -0.1 0.01 0.3 0.15 -0.1 0.1 0.2 0.01 -0.1 0.1 ]\n" ] } ], "source": [ "print(theta)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "empty_row = {}\n", "for c in actions:\n", " empty_row[c] = 0" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "{'campaign_e': 0, 'men_30_design_a': 0, 'men_20_design_c': 0, 'campaign_a': 0, 'female_20_design_c': 0, 'female_20_design_b': 0, 'female_20_font_b': 0, 'female_20_design_a': 0, 'female_20_design_d': 0, 'men_20_design_a': 0, 'female_30_design_d': 0, 'female_30': 0, 'campaign_c': 0, 'campaign_b': 0, 'female_30_font_b': 0, 'men_20_font_b': 0, 'men_30_design_c': 0, 'men_20_font_a': 0, 'female_30_design_c': 0, 'campaign_d': 0, 'men_30_font_b': 0, 'female_30_design_a': 0, 'female_30_font_a': 0, 'female_20': 0, 'men_20_design_b': 0, 'female_30_design_b': 0, 'men_30_font_a': 0, 'female_20_font_a': 0, 'men_20': 0, 'men_30_design_d': 0, 'men_20_design_d': 0, 'men_30': 0, 'campaign_f': 0, 'men_30_design_b': 0}\n" ] } ], "source": [ "print(empty_row)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "ret = []\n", "for k, v in campaigns.items():\n", " cp = k\n", " cp_value = v\n", " for k, v in attribute.items():\n", " attr = k\n", " attr_value = v\n", " for k, v in contextual_attrs[attr]['design'].items():\n", " design = k\n", " design_value = v\n", " for k, v in contextual_attrs[attr]['font'].items():\n", " font = k\n", " font_value = v\n", " row = empty_row.copy()\n", " row[cp] = 1\n", " row[attr] = 1\n", " row[attr + '_design_' + design] = 1\n", " row[attr + '_font_' + font] = 1\n", " ret.append(row)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 選択可能なactionの組み合わせ" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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"metadata": {}, "output_type": "execute_result" } ], "source": [ "df_actions = pd.DataFrame.from_dict(ret)\n", "df_actions = df_actions[actions]\n", "df_actions" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# コンテキストの生成\n", "contexts = [k for k in attribute.keys()]\n", "def get_context(t):\n", " return contexts[t % len(contexts)]" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# 0 or 1 の報酬を返す関数\n", "def calc_reward_proba(action):\n", " exp_theta_T_action = np.exp(theta.dot(action))\n", " probability = exp_theta_T_action/(1 + exp_theta_T_action)\n", " return probability\n", "\n", "def get_reward(action):\n", " return np.random.binomial(1, calc_reward_proba(action), 1)[0]" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CTR for action 0 = 0.0241270214177\n", "CTR for action 1 = 0.0218812709361\n", "CTR for action 2 = 0.0268571187848\n", "CTR for action 3 = 0.0243635943153\n", "CTR for action 4 = 0.0322954646985\n", "CTR for action 5 = 0.0293122307514\n", "CTR for action 6 = 0.0293122307514\n", "CTR for action 7 = 0.0265969935769\n", "CTR for action 8 = 0.0355711892726\n", "CTR for action 9 = 0.0293122307514\n", "CTR for action 10 = 0.0295981041791\n", "CTR for action 11 = 0.0243635943153\n", "CTR for action 12 = 0.0265969935769\n", "CTR for action 13 = 0.0218812709361\n", "CTR for action 14 = 0.0329263947981\n", "CTR for action 15 = 0.0271197172018\n", "CTR for action 16 = 0.0218812709361\n", "CTR for action 17 = 0.0265969935769\n", "CTR for action 18 = 0.0243635943153\n", "CTR for action 19 = 0.0295981041791\n", "CTR for action 20 = 0.0322954646985\n", "CTR for action 21 = 0.0391657227968\n" ] } ], "source": [ "for i in range(22):\n", " print('CTR for action', i ,'=', calc_reward_proba(df_actions.iloc[i].values))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## LinUCB\n", "\n", "118頁，アルゴリズム7.1\n", "\n", "入力: 誤差項の分散 $\\sigma^2$ \n", "パラメータ: $\\sigma_0^2, \\alpha > 0$\n", "\n", "$\n", "A^{-1} \\leftarrow \\frac{\\sigma^2_0}{\\sigma^2}I_d. \\ //\\ |a|*|a|の行列\\\\\n", "b \\leftarrow 0. \\ //\\ サイズ |a| のベクトル \\\\\n", "\\mathrm{for}\\ t = 1,2,....,T\\ \\mathrm{do} \\\\\n", "\\hspace{10pt}\\hat{\\theta} \\leftarrow A^{-1}b. \\\\\n", "\\hspace{10pt}//\\ 各行動iについてUCBスコアの計算，ただし \\alpha_t = \\alpha\\sqrt{logt} \\\\\n", "\\hspace{10pt}\\overline{\\mu_i} = a_{i,t}^{\\mathrm{T}}\\hat{\\theta} + \\alpha_t\\sigma\\sqrt{a_{i,t}^{\\mathrm{T}}A^{-1}a_{i,t}}\\\\\n", "\\hspace{10pt}スコア最大の行動\\ i\\ \\leftarrow\\ argmax_i\\overline{\\mu_i}_(t) を選択して報酬 X(t) を観測 \\\\\n", "\\hspace{10pt}A^{-1} \\leftarrow A^{-1} - \\frac{A^{-1}a_{i,t}^{\\mathrm{T}}A^{-1}}{1 + a_{i,t}^{\\mathrm{T}}A^{-1}a_{i,t}}. \\\\\n", "\\hspace{10pt}b \\leftarrow b + a_{i,t}X(t). \\\\\n", "\\mathrm{end\\ for}\n", "$" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def calc_new_a_inv(A_inv, a_i_t):\n", " return A_inv - (A_inv*(np.matrix(a_i_t).T)*(a_i_t)*A_inv)/(1 + a_i_t.dot(A_inv).dot(a_i_t))" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def linucb(T=1000, input_sigma2=600, param_sigma02=0.01, param_alpha=10):\n", " A_inv = np.matrix((param_sigma02/input_sigma2)*np.identity(len(actions)))\n", " b = np.zeros(len(theta)) \n", "\n", " # results\n", " rewards = []\n", " for t in range(1, T):\n", " alpha_t = param_alpha*np.sqrt(np.log(t))\n", " theta_hat = A_inv.A.dot(b)\n", " context = get_context(t)\n", " ucb_scores = []\n", " selectable_actions = []\n", " for i in df_actions[df_actions[context] != 0].index.values:\n", " a_i = df_actions.iloc[i].values\n", " ucb_score = a_i.dot(theta_hat) + alpha_t*np.sqrt(input_sigma2)*np.sqrt(a_i.dot(A_inv).dot(a_i))\n", " selectable_actions.append(a_i)\n", " ucb_scores.append(ucb_score)\n", " # 時刻tにおける行動 a_{i,t}\n", " a_i_t = selectable_actions[np.array(ucb_scores).argmax()]\n", " # 時刻tに観測した報酬\n", " reward = get_reward(a_i_t)\n", " b += a_i_t*reward\n", " A_inv = calc_new_a_inv(A_inv, a_i_t)\n", " rewards.append(reward)\n", " return theta_hat, np.array(rewards), b" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def run_linucb_test(T, trial, param_sigma02=0.0001, param_alpha=10, plot=True):\n", " rewards_result = []\n", " loss_result = []\n", " for _ in range(trial):\n", " theta_hat, rewards, b = linucb(T=T, param_sigma02=param_sigma02, param_alpha=param_alpha)\n", " loss = sum(theta - theta_hat)\n", " rewards_result.append(rewards.cumsum())\n", " loss_result.append(loss)\n", " \n", " reward_gained_mean = np.array(rewards_result).mean(axis=0)\n", " if plot:\n", " plt.figure(figsize=(14, 2))\n", " plt.xlabel('time')\n", " plt.ylabel('Average Rewards')\n", " plt.plot(reward_gained_mean)\n", " print('Theta - ThetaHat:{}'.format(np.mean(loss_result)))\n", " return reward_gained_mean" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Theta - ThetaHat:-12.940000933321034\n" ] }, { "data": { "image/png": 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XcnLyt44vLi7WXXfdpSVLlighIcHZVQDtyNi2zFMPSV99Kd/t98qKjHI7EgAA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\nALiGphQAAAAA4BqaUgAAAACAa/4/V93hSGLq+9YAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rewards = run_linucb_test(T=100, trial=10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## パラメータチューニング" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Theta - ThetaHat:-12.940029188144218\n", "Theta - ThetaHat:-12.940029188705498\n", "Theta - ThetaHat:-12.940027729077604\n", "Theta - ThetaHat:-12.940027995763927\n" ] } ], "source": [ "T = 1500\n", "rewards_1 = run_linucb_test(T=T, trial=5, param_alpha=0.5, plot=False)\n", "rewards_2 = run_linucb_test(T=T, trial=5, param_alpha=1, plot=False)\n", "rewards_3 = run_linucb_test(T=T, trial=5, param_alpha=10, plot=False)\n", "rewards_4 = run_linucb_test(T=T, trial=5, param_alpha=50, plot=False)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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8/KOlyrWsLCxPxoAq/u6dfu9FGu++H3u33WS/8EK1x1XT3TWJ6O2kYcOGxMTE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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(14, 4))\n", "plt.plot(rewards_1, color='b', label='alpha=0.5')\n", "plt.plot(rewards_2, color='g', label='alpha=1')\n", "plt.plot(rewards_3, color='r', label='alpha=10')\n", "plt.plot(rewards_4, color='y', label='alpha=50')\n", "plt.ylabel('AVG Reward')\n", "plt.xlabel('t')\n", "plt.legend(loc='best')\n", "plt.title(u'LinUCB 獲得報酬の比較 T={}'.format(T))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 正規分布モデルのThompson抽出\n", "\n", "121頁, アルゴリズム7.2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "入力: 誤差項の分散 $\\sigma^2$ \n", "パラメータ: $\\sigma_0^2 > 0$\n", "\n", "$\n", "A^{-1} \\leftarrow \\frac{\\sigma^2_0}{\\sigma^2}I_d. \\ //\\ |a|*|a|の行列\\\\\n", "b \\leftarrow 0. \\ //\\ サイズ |a| のベクトル \\\\\n", "\\mathrm{for}\\ t = 1,2,....,T\\ \\mathrm{do} \\\\\n", "\\hspace{10pt}\\tilde{\\theta}\\ を多変量正規分布\\ N(A^{-1}b, \\sigma^2A^{-1})\\ から生成. \\\\\n", "\\hspace{10pt}i \\leftarrow argmax_i\\tilde{\\theta}^{\\mathrm{T}}_a{i,t} を選択して報酬 X(t) を観測. \\\\\n", "\\hspace{10pt}A^{-1} \\leftarrow A^{-1} - \\frac{A^{-1}a_{i,t}^{\\mathrm{T}}A^{-1}}{1 + a_{i,t}^{\\mathrm{T}}A^{-1}a_{i,t}}. \\\\\n", "\\hspace{10pt}b \\leftarrow b + a_{i,t}X(t). \\\\\n", "\\mathrm{end\\ for}\n", "$" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def thompson_sampling(T=1000, input_sigma2=0.0001, param_sigma02=0.0001):\n", " A_inv = np.matrix((param_sigma02/input_sigma2)*np.identity(len(actions)))\n", " b = np.zeros(len(theta))\n", "\n", " # results\n", " rewards = []\n", " for t in range(1, T):\n", " theta_hat = np.random.multivariate_normal(A_inv.A.dot(b), input_sigma2*A_inv)\n", " context = get_context(t)\n", " estimated_rewards = []\n", " selectable_actions = []\n", " for i in df_actions[df_actions[context] != 0].index.values:\n", " a_i = df_actions.iloc[i].values\n", " estimated_reward = a_i.T.dot(theta_hat)\n", " selectable_actions.append(a_i)\n", " estimated_rewards.append(estimated_reward)\n", " # 時刻tにおける行動 a_{i,t}\n", " a_i_t = selectable_actions[np.array(estimated_rewards).argmax()]\n", " # 時刻tに観測した報酬\n", " reward = get_reward(a_i_t)\n", " b += a_i_t*reward\n", " A_inv = calc_new_a_inv(A_inv, a_i_t)\n", " rewards.append(reward)\n", " return theta_hat, np.array(rewards), b" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def run_thompson_test(T, trial, param_sigma02=0.0002, plot=True):\n", " rewards_result = []\n", " loss_result = []\n", " for _ in range(trial):\n", " theta_hat, rewards, b = thompson_sampling(T=T, param_sigma02=param_sigma02)\n", " loss = sum(theta - theta_hat)\n", " rewards_result.append(rewards.cumsum())\n", " loss_result.append(loss)\n", " \n", " reward_gained_mean = np.array(rewards_result).mean(axis=0)\n", " if plot:\n", " plt.figure(figsize=(14, 2))\n", " plt.xlabel('time')\n", " plt.ylabel('Average Rewards')\n", " plt.plot(reward_gained_mean)\n", " print('Theta - ThetaHat:{}'.format(np.mean(loss_result)))\n", " return reward_gained_mean" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# T=50でテスト\n", "theta_hat, rewards, b = thompson_sampling(50)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n", " 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n", " 0., 0., 0., 0., 0., 0., 0., 0.])" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# 全ての項から報酬が発生している (選択した) 事を確認\n", "b" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ -1.11928297e-02, -1.77892210e-03, -2.14037646e-03,\n", " -6.11712082e-04, -6.87450085e-03, -5.60347365e-05,\n", " 1.69322129e-02, 1.81993519e-02, 5.72347531e-03,\n", " 6.92431434e-03, -8.20865242e-05, 5.11289416e-05,\n", " -2.56771664e-02, -6.39318767e-03, -1.58180877e-02,\n", " -2.18094271e-03, -1.30384186e-02, -1.26637600e-02,\n", " -6.88009762e-03, -2.78735671e-03, -5.32144574e-03,\n", " -1.07322016e-02, 4.71536553e-04, -3.75928989e-03,\n", " 4.77155708e-04, 2.80381836e-03, -2.69030179e-03,\n", " -1.11309979e-03, 4.98324918e-03, -1.75372965e-04,\n", " -8.96714512e-03, -1.24796596e-02, -4.88911282e-03,\n", " 3.89463886e-03])" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# t=50時点での\\theta_hat\n", "theta_hat" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Theta - ThetaHat:-12.914555355771643\n" ] }, { "data": { "image/png": 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qKqy1xMTE+DW5iDiHrSiDhoaWX/jNdryv/xu+2Xboczp3xVyShTnrHIwrrPVF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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rewards_result = run_thompson_test(T=500, trial=10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## パラメータチューニング" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Theta - ThetaHat:-12.954196151371482\n", "Theta - ThetaHat:-12.935081957413228\n", "Theta - ThetaHat:-12.89747114393224\n", "Theta - ThetaHat:-12.80601003976167\n" ] } ], "source": [ "T = 1500\n", "rewards_1 = run_thompson_test(T=T, trial=10, param_sigma02=0.00001, plot=False)\n", "rewards_2 = run_thompson_test(T=T, trial=10, param_sigma02=0.0001, plot=False)\n", "rewards_3 = run_thompson_test(T=T, trial=10, param_sigma02=0.001, plot=False)\n", "rewards_4 = run_thompson_test(T=T, trial=10, param_sigma02=0.01, plot=False)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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4uHRH06yfQc0LPglEhRBCCCGEEM8V2z17sD5xAvsVK8h89VWyvb0tzmdWrkxq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\nfV3nlaiqyraEbeTaczmWfoylUUvJzM/k2+7f8nD9h3FZr31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phBA3kgSiQgghhLitKOnp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TYUFOAcOZLC0aMJnX9+pZ/W652J37+E4uJxxMffgaYZSEsbgdPZeb/9jvXdmogeYfz68SzMWciU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\nuPEhx1m4ayH/+O4fd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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(14, 4))\n", "plt.plot(rewards_1, color='b', label='param_sigma02=0.00001')\n", "plt.plot(rewards_2, color='g', label='param_sigma02=0.0001')\n", "plt.plot(rewards_3, color='r', label='param_sigma02=0.001')\n", "plt.plot(rewards_4, color='y', label='param_sigma02=0.01')\n", "plt.ylabel('AVG Reward')\n", "plt.xlabel('t')\n", "plt.legend(loc='best')\n", "plt.title(u'Thonpson抽出 獲得報酬の比較 T={}'.format(T))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 比較用のepsilon greedy実装" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def epsilon_greedy(T=1000, epsilon=0.1):\n", " # results\n", " rewards = []\n", " selected_counts = np.zeros(len(df_actions))\n", " gained_rewards = np.zeros(len(df_actions))\n", " for t in range(1, T):\n", " context = get_context(t)\n", " estimated_rewards = []\n", " selectable_actions = []\n", " selectable_actions_idx = []\n", " for i in df_actions[df_actions[context] != 0].index.values:\n", " a_i = df_actions.iloc[i].values\n", " estimated_reward = gained_rewards[i]/selected_counts[i]\n", " selectable_actions.append(a_i)\n", " selectable_actions_idx.append(i)\n", " estimated_rewards.append(estimated_reward)\n", " # 時刻tにおける行動 a_{i,t}\n", " if np.random.rand() > epsilon:\n", " _idx = np.array(estimated_rewards).argmax()\n", " else:\n", " # 探索\n", " _idx = np.random.randint(len(selectable_actions))\n", " a_i_t = selectable_actions[_idx]\n", " action_idx = selectable_actions_idx[_idx]\n", " # 時刻tに観測した報酬\n", " reward = get_reward(a_i_t)\n", " rewards.append(reward)\n", " selected_counts[action_idx] += 1\n", " gained_rewards[action_idx] += reward\n", "\n", " return np.array(rewards), selected_counts" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def run_epsilon_greedy_test(T, trial, plot=True):\n", " rewards_result = []\n", " selected_counts_result = []\n", " for _ in range(trial):\n", " rewards, selected_counts = epsilon_greedy(T=T)\n", " rewards_result.append(rewards.cumsum())\n", " selected_counts_result.append(selected_counts)\n", " \n", " reward_gained_mean = np.array(rewards_result).mean(axis=0)\n", " selected_count_mean = np.array(selected_counts_result).mean(axis=0)\n", " if plot:\n", " plt.figure(figsize=(14, 2))\n", " plt.xlabel('time')\n", " plt.ylabel('Average Rewards')\n", " plt.plot(reward_gained_mean)\n", " return reward_gained_mean, selected_count_mean" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/tnishibayashi/.pyenv/versions/anaconda3-4.0.0/lib/python3.5/site-packages/ipykernel/__main__.py:13: RuntimeWarning: invalid value encountered in double_scalars\n" ] }, { "data": { "image/png": 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rTqOcFSdS3ooTLVq0iKbP9wfPzs4mJyfnnMYJqBAdO3Yss2fP5qtf/SqdO3cm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\nIiIiIiH1/wGtt5w8+BGl0gAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "_, selected_count = run_epsilon_greedy_test(1000, trial=10, plot=True)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 72.6, 10.4, 2.3, 1.9, 1.6, 1.7, 1.5, 1.3, 19.2,\n", " 1.8, 1.9, 1.6, 1.5, 1.2, 1.4, 7.1, 17. , 8.6,\n", " 1.8, 1.5, 4.1, 12.3, 1.6, 1.3, 4.6, 1.5, 1.5,\n", " 4.6, 1.5, 1.8, 1.4, 7.2, 1.3, 1.4, 3.5, 1.7,\n", " 13.7, 1.5, 5.3, 3.5, 19.6, 1.7, 4.4, 4.7, 2. ,\n", " 1.5, 1.3, 1.4, 23. , 19.7, 1.7, 1.9, 1.4, 1.6,\n", " 9.2, 1.3, 1.2, 24. , 1.3, 15.7, 1.4, 24.5, 1.3,\n", " 1.8, 4.4, 1.5, 1.5, 1.3, 1.5, 1.3, 1.3, 5.3,\n", " 1.1, 1.6, 1.4, 1.5, 14.8, 1.8, 17. , 1.3, 1.4,\n", " 1.1, 19.5, 15.9, 1.7, 1.2, 1.3, 1.3, 1.9, 7.9,\n", " 1.6, 1.5, 1.5, 1.2, 1.4, 1.6, 4.1, 1.3, 5.9,\n", " 1.8, 1.5, 10.4, 1.6, 1.6, 24.1, 11.7, 1.4, 7.2,\n", " 1.3, 3.6, 3. , 1.6, 1.7, 1.5, 6.1, 2.9, 21.4,\n", " 1.3, 1.1, 1.7, 1.4, 1.7, 1.7, 1.6, 1.5, 1.3,\n", " 1.8, 23.4, 1.5, 1.3, 1.7, 34.1, 14.6, 1.5, 7.1,\n", " 1.7, 4.6, 1.7, 1.5, 1.1, 12.1, 1.4, 1.3, 12.5,\n", " 1.4, 4.4, 16.6, 1.6, 9.9, 1.4, 1.1, 1.6, 1.6,\n", " 1.2, 14.3, 1.3, 10.1, 25.5, 1.4, 1.3, 1.6, 1.5,\n", " 3.4, 1.5, 1.5, 1.5, 1.6, 1.4, 19.2, 1.6, 1. ,\n", " 1.5, 1.8, 1.4, 19.2, 1.4, 1.6, 3.1, 1.7, 3. ,\n", " 7.7, 2.8, 1.3, 1.7, 1.3, 1.3, 1.6, 1.1, 1.5,\n", " 24.3, 12.5, 1.4])" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "selected_count" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## ロジスティック回帰モデル上のトンプソン抽出" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "125頁，アルゴリズム7.3" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def calc_gradient(theta, var, action_history):\n", " ret = []\n", " ret.append(theta/var)\n", "\n", " for action_i_s, reward in action_history:\n", " exp_theta_T_action_i_s = np.exp(theta.dot(action_i_s))\n", " ret.append((exp_theta_T_action_i_s*action_i_s)/(1 + exp_theta_T_action_i_s))\n", "\n", " for action_i_s, reward in action_history:\n", " if reward == 1:\n", " ret.append(action_i_s * -1)\n", " return np.array(ret).sum(axis=0)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def calc_hessian(theta, var, action_history):\n", " ret = []\n", " ret.append(np.identity(len(actions))/var)\n", "\n", " for action_i_s, reward in action_history:\n", " exp_theta_T_action_i_s = np.exp(theta.dot(action_i_s))\n", " ret.append((exp_theta_T_action_i_s*(np.matrix(action_i_s).T)*action_i_s)/(1+exp_theta_T_action_i_s)**2)\n", "\n", " return np.array(ret).sum(axis=0)" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def calc_theta_hat(theta_hat, var, action_history, traial=20):\n", " _theta_hat = theta_hat\n", " for _ in range(traial):\n", " hessian = calc_hessian(_theta_hat, 2, action_history)\n", " gradient = calc_gradient(_theta_hat, 2, action_history)\n", " _theta_hat = _theta_hat - np.linalg.inv(hessian).dot(gradient)\n", " return _theta_hat" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def thompson_sampling_on_logistic_regression(T=1000, param_sigma02=0.01):\n", " rewards = []\n", " action_history = []\n", " selected_counts = np.zeros(len(df_actions))\n", " theta_hat = np.zeros(len(actions))\n", " for t in range(1, T):\n", " if t % 20 == 1:\n", " # 20回に1度だけtheta_hatを更新\n", " # 毎回初期状態から計算しているので遅い……\n", " # TODO 勾配ベクトルとヘッセ行列は前回の計算過程を使い回す\n", " theta_hat = calc_theta_hat(theta_hat, param_sigma02, action_history)\n", " hessian = calc_hessian(theta_hat, param_sigma02, action_history)\n", " hessian_inv = np.linalg.inv(hessian)\n", "\n", " theta_tild = np.random.multivariate_normal(\n", " theta_hat,\n", " hessian_inv\n", " )\n", " context = get_context(t)\n", " estimated_rewards = []\n", " selectable_actions = []\n", " selectable_action_idx = []\n", " for i in df_actions[df_actions[context] != 0].index.values:\n", " a_i = df_actions.iloc[i].values\n", " selectable_actions.append(a_i)\n", " selectable_action_idx.append(i)\n", " estimated_rewards.append(a_i.T.dot(theta_tild))\n", " # 時刻tにおける行動 a_{i,t}\n", " argmax_i = np.array(estimated_rewards).argmax()\n", " a_i_t = selectable_actions[argmax_i]\n", " selected_i = selectable_action_idx[argmax_i]\n", " # 時刻tに観測した報酬\n", " reward = get_reward(a_i_t)\n", " action_history.append((a_i_t, reward))\n", " rewards.append(reward)\n", " selected_counts[selected_i] += 1\n", " return theta_hat, np.array(rewards), selected_counts" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def run_thompson_sampling_on_logistic_regression_test(T, trial, param_sigma02=0.01, plot=True):\n", " rewards_result = []\n", " selected_counts_result = []\n", " for _ in range(trial):\n", " theta_hat, rewards, selected_counts = thompson_sampling_on_logistic_regression(\n", " T=T,\n", " param_sigma02=param_sigma02)\n", " rewards_result.append(rewards.cumsum())\n", " selected_counts_result.append(selected_counts)\n", " \n", " reward_gained_mean = np.array(rewards_result).mean(axis=0)\n", " selected_count_mean = np.array(selected_counts_result).mean(axis=0)\n", " if plot:\n", " plt.figure(figsize=(14, 2))\n", " plt.xlabel('time')\n", " plt.ylabel('Average Rewards')\n", " plt.plot(reward_gained_mean)\n", " return reward_gained_mean, selected_count_mean" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [], "source": [ "rewards_1, selected_count = run_thompson_sampling_on_logistic_regression_test(2000, 10, param_sigma02=0.00001, plot=False)\n", "rewards_2, selected_count = run_thompson_sampling_on_logistic_regression_test(2000, 10, param_sigma02=0.0001, plot=False)\n", "rewards_3, selected_count = run_thompson_sampling_on_logistic_regression_test(2000, 10, param_sigma02=0.001, plot=False)\n", "rewards_4, selected_count = run_thompson_sampling_on_logistic_regression_test(2000, 10, param_sigma02=0.01, plot=False)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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84sSJata74AZTQUD41ltvUa9ePXWgqA0bNqj7obibQKVV1LERFhZGaGgoYWFh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\nb+0rLC9ZRNgXjbV0EK3rLuEPZ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(14, 4))\n", "plt.plot(rewards_1, color='b', label='param_sigma02=0.00001')\n", "plt.plot(rewards_2, color='g', label='param_sigma02=0.0001')\n", "plt.plot(rewards_3, color='r', label='param_sigma02=0.001')\n", "plt.plot(rewards_4, color='y', label='param_sigma02=0.01')\n", "plt.ylabel('AVG Reward')\n", "plt.xlabel('t')\n", "plt.legend(loc='best')\n", "plt.title(u'Logistic回帰モデル上のThonpson抽出 獲得報酬の比較 T=2000')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 比較" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/tnishibayashi/.pyenv/versions/anaconda3-4.0.0/lib/python3.5/site-packages/ipykernel/__main__.py:13: RuntimeWarning: invalid value encountered in double_scalars\n" ] } ], "source": [ "T=5000\n", "trial=10\n", "result_ep, selected_ep = run_epsilon_greedy_test(\n", " T=T, trial=trial, plot=False)" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Theta - ThetaHat:-12.940091487088731\n" ] } ], "source": [ "result_ucb = run_linucb_test(\n", " T=T, trial=trial, param_alpha=1, plot=False)" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Theta - ThetaHat:-12.854085700454869\n" ] } ], "source": [ "result_thompson = run_thompson_test(\n", " T=T, trial=trial, param_sigma02=0.001, plot=False)" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": true }, "outputs": [], "source": [ "result_logistic_thompson = run_thompson_sampling_on_logistic_regression_test(\n", " T=T, trial=trial, param_sigma02=0.1, plot=False)" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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oaDp37kxISAijRo1yXn/FY489RtWqVZ29zkIIIYQQQpQFm+08hYU/UFQUh92e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\norBwB1braazWJPT62ri41EZRXKhefS1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u6HRJGAypxMZOxWIZ2CLfz5rTqlVGPvgghK1b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\ns+L92daxt/V2dnaqtLRU4+PjC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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(14, 4))\n", "plt.plot(result_ep, color='b', label='Epsilon-Greedy')\n", "plt.plot(result_ucb, color='g', label='LinUCB')\n", "plt.plot(result_thompson, color='r', label='Thompson Sampling')\n", "plt.plot(result_logistic_thompson[0], color='y', label='Thompson Sampling on LR')\n", "plt.ylabel('AVG Reward')\n", "plt.xlabel('t')\n", "plt.legend(loc='best')\n", "plt.title(u'獲得報酬の比較 T={}'.format(T))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ロジスティック回帰モデルのThompson抽出が一番良くなった" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 }