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Created July 18, 2016 14:01
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201607_BanditsPlayground.ipynb
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"\n",
"import matplotlib\n",
"matplotlib.use('Qt5Agg')\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"import seaborn as sns"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# K-armed bernoulli bandit (non-contextualised)"
]
},
{
"cell_type": "code",
"execution_count": 220,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>failure</th>\n",
" <th>success</th>\n",
" </tr>\n",
" <tr>\n",
" <th>arm</th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>16</td>\n",
" <td>4</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>17</td>\n",
" <td>8</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>33</td>\n",
" <td>12</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>9</td>\n",
" <td>1</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" failure success\n",
"arm \n",
"1 16 4\n",
"2 17 8\n",
"3 33 12\n",
"4 9 1"
]
},
"execution_count": 220,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"true_probs = [0.2, .3, .4, .05]\n",
"n_arms = len(true_probs)\n",
"\n",
"arm_totals = np.array([20, 25, 45, 10])\n",
"arm_ks = np.random.binomial(n=arm_totals, p=true_probs)\n",
"arm_counts = pd.DataFrame.from_dict(\n",
" {'arm': np.arange(1, n_arms + 1), 'success': arm_ks, 'failure': arm_totals - arm_ks}).set_index('arm')\n",
"arm_counts"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Upper Confidence Bound 1\n",
"\n",
"\"Optimism in the face of uncertainty\", see https://www.cs.bham.ac.uk/internal/courses/robotics/lectures/ucb1.pdf\n",
"\n",
"At stage $t$, given observed successes and counts $k_j$ and $n_j$ for each arms, pick arm:\n",
"\n",
"$$ \\underset{j}{\\arg\\max} = \\frac{k_j}{n_j} + \\sqrt{ \\frac{2 n}{n_j} } $$"
]
},
{
"cell_type": "code",
"execution_count": 227,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>failure</th>\n",
" <th>success</th>\n",
" <th>mu</th>\n",
" <th>confidence</th>\n",
" <th>ucb</th>\n",
" </tr>\n",
" <tr>\n",
" <th>arm</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>16</td>\n",
" <td>4</td>\n",
" <td>0.200000</td>\n",
" <td>0.678614</td>\n",
" <td>0.878614</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>17</td>\n",
" <td>8</td>\n",
" <td>0.320000</td>\n",
" <td>0.606971</td>\n",
" <td>0.926971</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>33</td>\n",
" <td>12</td>\n",
" <td>0.266667</td>\n",
" <td>0.452409</td>\n",
" <td>0.719076</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>9</td>\n",
" <td>1</td>\n",
" <td>0.100000</td>\n",
" <td>0.959705</td>\n",
" <td>1.059705</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" failure success mu confidence ucb\n",
"arm \n",
"1 16 4 0.200000 0.678614 0.878614\n",
"2 17 8 0.320000 0.606971 0.926971\n",
"3 33 12 0.266667 0.452409 0.719076\n",
"4 9 1 0.100000 0.959705 1.059705"
]
},
"execution_count": 227,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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AAFRcu8W62267RUTEmjVr4pJLLonvfe97HZ7w/WUt5ZmMXYqfGwCgXAqlUqnU3gFLly6N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\nisAFACAVgQsAQCr/H5JrPFW3E0EfAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1103d8320>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"arm_colors = sns.color_palette()[:n_arms]\n",
"def ucb1_bounds(arm_counts):\n",
" arm_totals = arm_counts.sum(axis=1)\n",
" return arm_counts \\\n",
" .assign(mu= lambda df: df.div(arm_totals, axis=0).success) \\\n",
" .assign(confidence= lambda df: np.sqrt(2 * np.log(arm_totals.sum()) / arm_totals)) \\\n",
" .assign(ucb= lambda df: df.mu + df.confidence.values)\n",
"\n",
"ucb_arms = ucb1_bounds(arm_counts)\n",
"\n",
"plt.figure(figsize=(12, 8))\n",
"plt.barh(bottom=-ucb_arms.index, height=.01 * ucb_arms.sum(1), \n",
" width=ucb_arms.mu, color=arm_colors, xerr=ucb_arms.confidence.values, ecolor='grey')\n",
"plt.yticks(-ucb_arms.index, ucb_arms.index);\n",
"plt.xlim([0, 1.5])\n",
"plt.title('Deterministic UCB1');\n",
"\n",
"ucb_arms"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Bayesian and the beta-binomial conjugate\n",
"\n",
"$$ p_j \\sim Beta(k_j + \\alpha, (n_j - k_j) + \\beta) $$"
]
},
{
"cell_type": "code",
"execution_count": 228,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"success/failures\n"
]
},
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>failure</th>\n",
" <th>success</th>\n",
" </tr>\n",
" <tr>\n",
" <th>arm</th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>16</td>\n",
" <td>4</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>17</td>\n",
" <td>8</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>33</td>\n",
" <td>12</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>9</td>\n",
" <td>1</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" failure success\n",
"arm \n",
"1 16 4\n",
"2 17 8\n",
"3 33 12\n",
"4 9 1"
]
},
"execution_count": 228,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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Kd3ljfU13aSl7//gU7hInrV+bjdFctWteHnztzxTu3E7EtBlYmzWr0nvVFTV1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dRf7ClJkiR9Ppk0z6FxT4ih8QCLKnPQ1LR56a8rdHkR4Aw7Z3R5exgOjLKioBGblt7tBGdKURS2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\nJ/PO4yer3dgAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10e5bbef0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from scipy.stats import beta\n",
"\n",
"\n",
"plt.figure(figsize=(12, 8))\n",
"xs = np.linspace(0, 1, 1000)\n",
"\n",
"for j_arm, count_row in enumerate(arm_counts[['success', 'failure']].values):\n",
" dist_arm_j = beta(*(1 + count_row))\n",
" ys = dist_arm_j.pdf(xs) / 100\n",
" q95 = dist_arm_j.ppf(.95)\n",
" plt.vlines(q95, 0, dist_arm_j.pdf(q95) / 100, color=arm_colors[j_arm])\n",
" plt.fill_between(xs, 0, ys, where=xs>=q95, color=arm_colors[j_arm], alpha=.5, label='q95 for arm' + str(j_arm+1))\n",
" plt.plot(xs, ys, label='/'.join(count_row.astype(str)))\n",
" \n",
"plt.title('Bayes + deterministic UCB');plt.legend();\n",
"\n",
"arm_counts"
]
},
{
"cell_type": "code",
"execution_count": 278,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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gfzkzXl1xXMJ8rPx9bh59dQWF+8v9Ov7ixZl+7c/flDSLiIiItHHGGJ6Zu46yiurTur+s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KaD6uaBMZ1L1ukwzZ2Pr6sTT0N9aAKMEBlxaSxOL6PV0U55x8lwhyMIgiDcpKhImqO93dy5+j4U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\nR9hugCcvdtPR6+SWk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kwkzbeuLWL2wuyQn7u128G/vXaSHqubTcvzuXfF+CTm4y3o8dD+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\nQRjG/w/OxGjZ+8ZwIwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10e68df98>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from scipy.stats import beta\n",
"\n",
"plt.figure(figsize=(12, 8))\n",
"xs = np.linspace(0, 1, 1000)\n",
"\n",
"for j_arm, count_row in enumerate(arm_counts[['success', 'failure']].values):\n",
" dist_arm_j = beta(*(1 + count_row))\n",
" ys = dist_arm_j.pdf(xs) / 100\n",
"\n",
" theta_j = dist_arm_j.rvs()\n",
" plt.plot(theta_j, dist_arm_j.pdf(theta_j) / 100, 'o', color=arm_colors[j_arm], ms=15, label='$\\\\theta^t_j$')\n",
" plt.plot(xs, ys, label='/'.join(count_row.astype(str)))\n",
" \n",
"plt.title('Stochastic Thompson sampling');plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## On-line update"
]
},
{
"cell_type": "code",
"execution_count": 152,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"counts = np.zeros((n_arms, 2))"
]
},
{
"cell_type": "code",
"execution_count": 260,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Random sampling:\n",
"Arm 3 produced Failure reward\n"
]
},
{
"data": {
"image/png": 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XAwAAAEgKs9AsSWnD4mUYUm0lPxUCAAAgPIRfaM7sWjKv5iEnAAAACBNhF5o/ezMgAAAA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"text/plain": [
"<matplotlib.figure.Figure at 0x10e3d8080>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"print('Random sampling:')\n",
"sampled_arm = np.random.randint(len(true_probs))\n",
"reward = np.random.uniform() <= true_probs[sampled_arm]\n",
"counts[sampled_arm, 1 - reward] += 1\n",
"print('Arm {} produced {} reward'.format(sampled_arm, 'Success' if reward else 'Failure'))\n",
"plt.figure(figsize=(12, 8))\n",
"for count_row in counts:\n",
" ys = beta.pdf(xs, *(1 + count_row)) / 100\n",
" plt.plot(xs, ys, label='/'.join(count_row.astype(str))) \n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Periodical batch scenario\n",
"\n",
" * Our current set-up is based on pre-computed scores\n",
" * For diversification and exploration, it's important to not always recommend the same top N items\n",
" * Those scores are normalised into a Probability Mass Function and sampled from at each query\n",
" * (Ref Yahoo article?)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Sampling from popularity scores\n",
"\n",
"Randomization, similar idea to Thompson sampling, except we directly sample articles"
]
},
{
"cell_type": "code",
"execution_count": 347,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>views</th>\n",
" <th>score</th>\n",
" </tr>\n",
" <tr>\n",
" <th>articleId</th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>11</th>\n",
" <td>2228</td>\n",
" <td>0.262210</td>\n",
" </tr>\n",
" <tr>\n",
" <th>27</th>\n",
" <td>1340</td>\n",
" <td>0.157703</td>\n",
" </tr>\n",
" <tr>\n",
" <th>29</th>\n",
" <td>721</td>\n",
" <td>0.084853</td>\n",
" </tr>\n",
" <tr>\n",
" <th>24</th>\n",
" <td>720</td>\n",
" <td>0.084736</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>615</td>\n",
" <td>0.072378</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" views score\n",
"articleId \n",
"11 2228 0.262210\n",
"27 1340 0.157703\n",
"29 721 0.084853\n",
"24 720 0.084736\n",
"2 615 0.072378"
]
},
"execution_count": 347,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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2+nyj8V67PHTo0Jx77rmZNGlSampq0tDQ0LYk3ogRIzJu3LjMnDmz7fYHHHBATj755Jx8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\nAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x110bf2358>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"n_articles = 50\n",
"topn = 10\n",
"article_overall_counts = pd.DataFrame.from_dict(\n",
" {'articleId': 1 + np.arange(n_articles), 'views': (np.random.pareto(5, size=n_articles) * 1000).astype(int)}\n",
" ).set_index('articleId').sort_values('views', ascending=False)\n",
"\n",
"topn_views_cutoff = article_overall_counts.views.iloc[topn] \n",
"article_overall_counts['score'] = article_overall_counts.views * (article_overall_counts.views >= topn_views_cutoff).astype(float)\n",
"article_overall_counts.score = article_overall_counts.score.div(article_overall_counts.score.sum())\n",
"plt.figure(figsize=(12, 8))\n",
"plt.barh(bottom=-np.arange(topn), width=article_overall_counts.score.iloc[:topn])\n",
"plt.yticks(-np.arange(topn) + .25, article_overall_counts.iloc[:topn].index);\n",
"plt.title('Popularity scores as a Probability function');\n",
"\n",
"article_overall_counts.sort_values('views', ascending=False).head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Contextual improvement\n",
"\n",
"LinUCB from [A Contextual-Bandit Approach to\n",
"Personalized News Article Recommendation](www.research.rutgers.edu/~lihong/pub/Li10Contextual.pdf). For a given step $t$, and for each arm/article candidate $a$:\n",
"\n",
"$$ \\mathbb{E}[r_{a, t} | \\mathbf{x}_{a, t}] = \\mathbf{x}_{a, t}^\\top \\mathbf{\\theta}_a^{\\star} $$\n",
"\n",
"$ \\mathbf{\\theta}_a^{\\star} \\in \\mathbb{R}^d$ are estimated from $n$ past contexts $\\mathbf{X_a}$ and observed rewards (i.e. clicks) $\\mathbf{y}_a$\n",
"\n",
"$$\\hat{\\theta}_a = \\underbrace{(\\mathbf{X_a}^\\top \\mathbf{X_a} + \\lambda \\mathbf{I})^{-1}}_{\\mathbf{A_a^{-1}}} \\mathbf{X_a}^\\top \\mathbf{y}_a $$ \n",
"\n",
"At a given step $t$, pick arm $a_t$ such as:\n",
"\n",
"$$ a_t = \\underset{a \\in \\mathcal{A}_t}{\\arg\\max} \\ \\mathbf{x}_{a, t}^\\top \\hat{\\mathbf{\\theta}}_a + \\alpha \\sqrt{ \\mathbf{x}_{a, t}^\\top \\mathbf{A_a}^{-1} \\mathbf{x}_{a, t}}$$\n",
"\n",
" * In practise, user and article features are built as an off-line pre-processing step\n",
" * The users are projected and grouped into an induced space of articles, so that user features loosely correspond to membership into category of content (see 5.2.2 Feature construction) \n",
" * In the simplest, disjoint model, $\\mathbf{x}_{a, t}$ just contains condensed user features ($d = 6$!)\n",
" * The article features are the $\\mathbf{\\theta}_a^{\\star}$ learnt for each arm $a$\n",
" * For a small pool of candidate arms ($\\approx 30$), this disjoint model proved to be equivalent to a more sophisticated model with a global component."
]
},
{
"cell_type": "code",
"execution_count": 642,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>cooking</th>\n",
" <th>video-game</th>\n",
" </tr>\n",
" <tr>\n",
" <th>user</th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>teenager</th>\n",
" <td>-0.2</td>\n",
" <td>0.3</td>\n",
" </tr>\n",
" <tr>\n",
" <th>granny</th>\n",
" <td>0.4</td>\n",
" <td>-0.4</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" cooking video-game\n",
"user \n",
"teenager -0.2 0.3\n",
"granny 0.4 -0.4"
]
},
"execution_count": 642,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Toy set-up d=2\n",
"\n",
"user_features = pd.DataFrame.from_records(\n",
" [{'user': 'teenager', 'video-game': .7, 'cooking': -.5},\n",
" {'user': 'granny', 'video-game': -.3, 'cooking': .8}], \n",
" index='user')\n",
"\n",
"user_features"
]
},
{
"cell_type": "code",
"execution_count": 643,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>cooking</th>\n",
" <th>video-game</th>\n",
" </tr>\n",
" <tr>\n",
" <th>article</th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>Pokemon go craze</th>\n",
" <td>-1.0</td>\n",
" <td>1.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Cooking mama 3 is out</th>\n",
" <td>0.4</td>\n",
" <td>0.9</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" cooking video-game\n",
"article \n",
"Pokemon go craze -1.0 1.0\n",
"Cooking mama 3 is out 0.4 0.9"
]
},
"execution_count": 643,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"article_hidden_features = pd.DataFrame.from_records(\n",
" [{'article': 'Pokemon go craze', 'video-game': 1, 'cooking': -1},\n",
" {'article': 'Cooking mama 3 is out', 'video-game': .9, 'cooking': .4},\n",
" #{'article': 'Brexit is a hoax', 'video-game': .1, 'cooking': .1}\n",
" ], \n",
" index='article')\n",
"\n",
"article_hidden_features"
]
},
{
"cell_type": "code",
"execution_count": 645,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th>article</th>\n",
" <th>Pokemon go craze</th>\n",
" <th>Cooking mama 3 is out</th>\n",
" </tr>\n",
" <tr>\n",
" <th>user</th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>teenager</th>\n",
" <td>0.5</td>\n",
" <td>0.19</td>\n",
" </tr>\n",
" <tr>\n",
" <th>granny</th>\n",
" <td>-0.8</td>\n",
" <td>-0.20</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
"article Pokemon go craze Cooking mama 3 is out\n",
"user \n",
"teenager 0.5 0.19\n",
"granny -0.8 -0.20"
]
},
"execution_count": 645,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"true_expected_payoffs = pd.DataFrame(\n",
" user_features.values.dot(article_hidden_features.T),\n",
" index=user_features.index, columns=article_hidden_features.index)\n",
"\n",
"true_expected_payoffs"
]
},
{
"cell_type": "code",
"execution_count": 790,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 1.],\n",
" [-1.]])"
]
},
"execution_count": 790,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# noise modelling click uncertainty and unexplained\n",
"epsilon = .2\n",
"\n",
"def simulated_click(x_features, theta_arm, epsilon):\n",
" n_trials = x_features.shape[0]\n",
"\n",
" expected_ctrs = x_features.dot(theta_arm)\n",
" random_noises = np.random.normal(scale=epsilon, size=n_trials)\n",
" pay_offs_prob_trials = expected_ctrs + random_noises\n",
"\n",
" # sampling uniform between -1 and 1\n",
" y_trials = 2 * ((np.random.uniform(low=-1, high=1, size=len(expected_ctrs)) <= pay_offs_prob_trials) - .5) \n",
" return y_trials.reshape((n_trials, 1))\n",
"\n",
"simulated_click(\n",
" x_features = user_features.values,\n",
" theta_arm = article_hidden_features.loc['Pokemon go craze'].values, epsilon=.2)"
]
},
{
"cell_type": "code",
"execution_count": 795,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"def random_clicks(arm_article, n_training=20, article_hidden_features=article_hidden_features):\n",
" x_features = np.random.uniform(low=-1, high=1, size=(n_training, 2))\n",
" y_clicks = simulated_click(x_features, \n",
" theta_arm = article_hidden_features.loc[arm_article].values, epsilon=0.1)\n",
" \n",
" training_clicks = pd.DataFrame(\n",
" data=np.hstack([x_features, y_clicks]), \n",
" columns=user_features.columns.tolist() + ['clicked']) \\\n",
" .rename_axis(['training user'])\n",
" return training_clicks\n",
"\n",
"\n",
"def linear_fit(training_clicks):\n",
" feature_columns = ['cooking', 'video-game']\n",
" x_features = training_clicks[feature_columns]\n",
" covariance_inverse = np.linalg.inv(np.dot(x_features.T, x_features))\n",
" estimated_arm_features = np.dot(covariance_inverse, np.dot(x_features.T, training_clicks.clicked))\n",
" fitted_training_clicks = training_clicks.assign(estimated_clicked=lambda _:x_features.dot(estimated_arm_features))\n",
" return fitted_training_clicks, estimated_arm_features, covariance_inverse\n",
"\n",
"import matplotlib.cm as cm\n",
"def plot_training_clicks(training_clicks):\n",
" clicked = training_clicks.clicked == 1.0\n",
" plt.scatter(training_clicks[clicked]['cooking'], training_clicks[clicked]['video-game'], c='red', \n",
" cmap=cm.rainbow, marker='v', edgecolors='face', label='Clicked')\n",
" plt.scatter(training_clicks[~clicked]['cooking'], training_clicks[~clicked]['video-game'], c='blue',\n",
" cmap=cm.rainbow, marker='o', edgecolors='face', label='NOT clicked')\n",
"\n",
" \n",
"def plot_contour(z_grid, x_grid=x_grid, y_grid=y_grid, cmap=cm.rainbow):\n",
" c = plt.contour(x_grid, y_grid, z_grid, cmap=cm.rainbow)\n",
" plt.clabel(c, inline=1, fontsize=10);"
]
},
{
"cell_type": "code",
"execution_count": 803,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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O9jEiZ72jnE8DKwipUTqFUxlZ0x237djzHYUQB86JJ2LKcHQhRBshn76FEG1K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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10e611470>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"arm_article = 'Cooking mama 3 is out'\n",
"\n",
"training_clicks = random_clicks(arm_article, n_training=20)\n",
"\n",
"fitted_training_clicks, estimated_arm_features, covariance_inverse = linear_fit(training_clicks)\n",
"\n",
"x_grid, y_grid = np.meshgrid(np.linspace(-1, 1), np.linspace(-1, 1))\n",
"x_features_grid = np.vstack([x_grid.ravel(), y_grid.ravel()]).T\n",
"y_hat_grid = x_features_grid.dot(estimated_arm_features).reshape(x_grid.shape)\n",
"\n",
"y_hat_std_grid = np.sqrt(np.diag(np.dot(\n",
" np.dot(x_features_grid, covariance_inverse),\n",
" x_features_grid.T))).reshape(x_grid.shape)\n",
"\n",
"plt.figure(figsize=(18, 6))\n",
"plt.subplot(1, 3, 1)\n",
"plot_training_clicks(training_clicks)\n",
"plot_contour(z_grid=y_hat_grid)\n",
"plt.xlabel('cooking')\n",
"plt.ylabel('video-game')\n",
"plt.legend()\n",
"plt.subplot(1, 3, 2)\n",
"plt.title(arm_article)\n",
"plot_contour(z_grid=y_hat_std_grid)\n",
"plt.subplot(1, 3, 3)\n",
"plot_contour(z_grid=y_hat_std_grid + y_hat_grid)"
]
},
{
"cell_type": "code",
"execution_count": 798,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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WNR2Db7M2scy9FdmU6BJpTMd4A+Qa/p4lXlkZxP6fj/EO+yOGP1D+RiKWXjy8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\nKy6PGDGKZ599mqFDr0VRFLx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r3JLiujmUErY6Wo0kihVHQV2xHO/ddxB5bAyp8waA3Q7p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\nEEIIIYQQQmQVKVYIIYQQQgghhBAiq/x/NnWYCEF32v0AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10eec7438>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"arm_article = 'Pokemon go craze'\n",
"\n",
"training_clicks = random_clicks(arm_article, n_training=40)\n",
"\n",
"fitted_training_clicks, estimated_arm_features, covariance_inverse = linear_fit(training_clicks)\n",
"\n",
"x_grid, y_grid = np.meshgrid(np.linspace(-1, 1), np.linspace(-1, 1))\n",
"x_features_grid = np.vstack([x_grid.ravel(), y_grid.ravel()]).T\n",
"y_hat_grid = x_features_grid.dot(estimated_arm_features).reshape(x_grid.shape)\n",
"\n",
"y_hat_std_grid = np.sqrt(np.diag(np.dot(\n",
" np.dot(x_features_grid, covariance_inverse),\n",
" x_features_grid.T))).reshape(x_grid.shape)\n",
"\n",
"plt.figure(figsize=(18, 6))\n",
"plt.subplot(1, 3, 1)\n",
"plot_training_clicks(training_clicks)\n",
"plot_contour(z_grid=y_hat_grid)\n",
"plt.xlabel('cooking')\n",
"plt.ylabel('video-game')\n",
"plt.legend()\n",
"plt.subplot(1, 3, 2)\n",
"plt.title(arm_article)\n",
"plot_contour(z_grid=y_hat_std_grid)\n",
"plt.subplot(1, 3, 3)\n",
"plot_contour(z_grid=y_hat_std_grid + y_hat_grid)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"plt.con"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Logistic regression based\n",
"\n",
"Empirical comparison of LinUCB and Thompson sampling for display advertising and news recommendations from [An Empirical Evaluation of Thompson Sampling](www.research.rutgers.edu/~lihong/pub/Chapelle12Empirical.pdf)"
]
},
{
"cell_type": "code",
"execution_count": 735,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"plt.scatter?"
]
},
{
"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": "3.5.0"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
@DaveStudent
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201607_BanditsPlayground.ipynb

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