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Last active September 16, 2020 21:48
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A Jupyter Notebook taking a look at the multi-armed bandit problem.
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Those Ignorant, One-Armed Bandits\n",
"\n",
"I've been thinking a lot about the [multi-armed bandit](https://en.wikipedia.org/wiki/Multi-armed_bandit) problem lately. Here's the description from Wikipedia:\n",
"\n",
"> In probability theory, the multi-armed bandit problem is a problem in which a gambler at a row of slot machines (sometimes known as \"one-armed bandits\") has to decide which machines to play, how many times to play each machine and in which order to play them. When played, each machine provides a random reward from a probability distribution specific to that machine. The objective of the gambler is to maximize the sum of rewards earned through a sequence of lever pulls.\n",
" \n",
"I'm especially interested in this problem because I think it's a good exercise for thinking about how society should allocate scarce resources. For example, when trying to combat an infectious disease we should spend a substantial amount on the immmediate response. But we also need to invest in research on long-term solutions like vaccines and diagnostic tools even if these outcomes are more uncertain. How do we decide how much to allocate to each of these areas over time? This explore-exploit tradeoff is what makes these types of problems difficult to solve. \n",
"\n",
"The traditional problem above has some good solutions but I recently thought of a twist that hasn't been researched yet: What if you only know the collective score of a group of machines each round rather than the score of each individual machine (each individual is \"ignorant\" of it's own score)? This seems to be precisely the problem we have in many policy situations: we change some policy but we're not sure if the effect we observe is due to our change, some other change (possibly from a different time step), or random noise. Running a [randomized trial](https://en.wikipedia.org/wiki/Randomized_controlled_trial) (RCT) can help cancel out the random noise and other effects, but even RCTs have issues with applicability, external validity, and scale.\n",
"\n",
"Below I lay out the problem in Python and propose a few initial solutions, one of which converges. For now, I limit the effect of each machine to a single time step and only change one at a time. This isn't as complicated as reality but it allows me to reach an initial solution."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"\n",
"import random\n",
"from collections import namedtuple\n",
"import statistics\n",
"\n",
"import matplotlib.pyplot as plt\n",
"import matplotlib"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Initial Approach\n",
"\n",
"My initial approach to solving this problem is to just select five random machines, get a score, then replace one of them at random. If the resulting score is an improvement, I keep the new selection of machines for the next step. This approach works fairly well, but it never converges because I am always randomly replacing a machine, reducing the score. "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def run_simple_simulation(num_levers, num_selected, steps):\n",
" score = 0\n",
" mus = list(range(1,num_levers+1))\n",
" sigmas = list(1 for i in range(num_levers))\n",
" Lever = namedtuple('Lever', ['mu', 'sigma'])\n",
" levers = [Lever(mu=x[0], sigma=x[1]) for x in zip(mus, sigmas)]\n",
"\n",
" #Initialize\n",
" sample = random.sample(levers, num_selected)\n",
" score = sum([random.gauss(lever.mu, lever.sigma) for lever in sample])\n",
" history = [score]\n",
" optimal_score = levers[-1].mu*num_selected\n",
" regret = [optimal_score-score]\n",
"\n",
" for i in range(2,steps+1):\n",
" new_sample = list(sample) \n",
" new_sample[random.choice(range(num_selected))] = random.choice(levers) \n",
" new_score = sum([random.gauss(l.mu, l.sigma) for l in new_sample])\n",
"\n",
" if new_score > score:\n",
" score = new_score\n",
" sample = new_sample\n",
" \n",
" history.append(new_score)\n",
" regret.append(optimal_score*i-sum(history))\n",
" \n",
" return {\"sample\": sample, \"history\": history, \n",
" \"regret\": regret, \"levers\": levers}\n",
"\n",
"def display_results(result): \n",
" #https://stackoverflow.com/questions/1358977\n",
" fig, axes = plt.subplots(nrows=1, ncols=2, sharex=False, sharey=False, figsize=(15,7))\n",
" ax1 = axes[0]\n",
" ax1.plot(range(len(result[\"history\"])), result[\"history\"]) \n",
" ax1.set_xlabel('Step')\n",
" ax1.set_ylabel('Score')\n",
"\n",
" ax2 = axes[1]\n",
" ax2.plot(range(len(result[\"regret\"])), result[\"regret\"]) \n",
" ax2.set_xlabel('Step')\n",
" ax2.set_ylabel('Regret')\n",
" plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Selected Levers:\n",
"Mu: 99\n",
"Mu: 100\n",
"Mu: 100\n",
"Mu: 99\n",
"Mu: 99\n"
]
},
{
"data": {
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IUYj5DSdNun2q+9xbE8Zlr8zAhp2xFzHk9kkQBEE0dKpqIxjz4yoc+9gkrNxWgRcuHYIb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H5Zrb36KvBPAy9mx/cB4yKic0QMB0YCE0sVH0DKhv4s+CJJ0rq5599zGNS7C3s53VOSWrxSfkS3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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10c1612b0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"simple_result = run_simple_simulation(num_levers=100, num_selected=5, steps=1000)\n",
"\n",
"print(\"Selected Levers:\")\n",
"for lever in simple_result[\"sample\"]:\n",
" print(\"Mu: {0}\".format(lever.mu))\n",
"\n",
"display_results(simple_result)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Improved Solution\n",
"\n",
"To get around the non-convergence of the initial approach, I add a history of deltas to each machine. Think of the history as the changes \"caused\" by each machine when it's added to an existing group. So I start by selecting and pulling five levers, then replace the worst performing one with the best performing lever left out, then re-score the results with the new lever. The score change is added to the new machine's deltas, and then the process above is repeated until it settles on the best machine. \n",
"\n",
"In reality, it's impossible to know if the new machine actually caused the change observed in the score. This is because the new machine replaces an existing one and there's additional random noise from the probability distributions. The equation for this process would look something like this:\n",
"\n",
"`new_score = old_score - old_machine + new_machine + random_noise`\n",
"\n",
"I only know the `new_score` and `old_score` in this equation -- the rest are unknowns. But by assuming that the `new_machine_delta = new_score - old_score`, I am able to create a solution that converges on the best machine anyways. This approach is kind of like an experiment without a control group. I just assume the effect is entirely due to the machine I change. By repeating it enough times, it leads to a fairly accurate result even without a control."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def run_history_simulation(num_levers, num_selected, steps):\n",
" score = 0\n",
" mus = list(range(1, num_levers+1))\n",
" sigmas = list(1 for i in range(num_levers))\n",
" Lever = namedtuple('Lever', ['mu', 'sigma', 'deltas'])\n",
" levers = [Lever(mu=x[0], sigma=x[1], deltas=[]) for x in zip(mus, sigmas)]\n",
"\n",
" #Initialize\n",
" sample = random.sample(levers, num_selected)\n",
" score = sum([random.gauss(lever.mu, lever.sigma) for lever in sample])\n",
" history = [score]\n",
" optimal_score = levers[-1].mu*num_selected\n",
" regret = [optimal_score-score]\n",
" \n",
" for i in range(2,steps+1):\n",
" new_sample = list(sample) \n",
" old_lever = min(sample, key=lambda x : sum(x.deltas)/len(x.deltas) if x.deltas else 0) \n",
" new_lever = max(levers, key=lambda x : sum(x.deltas)/len(x.deltas) if x.deltas else 0)\n",
"\n",
" new_sample[new_sample.index(old_lever)] = new_lever \n",
" new_score = sum([random.gauss(l.mu, l.sigma) for l in new_sample])\n",
" new_lever.deltas.append(new_score-score)\n",
" if new_score > score:\n",
" score = new_score\n",
" sample = new_sample\n",
"\n",
" history.append(new_score)\n",
" regret.append(optimal_score*i-sum(history))\n",
" \n",
" return {\"sample\": sample, \"history\": history, \n",
" \"regret\": regret, \"levers\": levers}"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Selected Levers: \n",
"Mu: 100, Mean Delta: -5.6185\n",
"Mu: 100, Mean Delta: -5.6185\n",
"Mu: 100, Mean Delta: -5.6185\n",
"Mu: 100, Mean Delta: -5.6185\n",
"Mu: 100, Mean Delta: -5.6185\n"
]
},
{
"data": {
"image/png": 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oMOMXr2/CuuIqjM1Pw2s3nOZWjZiIogeDPwrZidpm3PzGpnbrl3x7GOUNZmQn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\nrcEh174jXVrDfj8AKFphrtsYkPRRd98gabOkW8xsg6TbJD3u7uskPR4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"text/plain": [
"<matplotlib.figure.Figure at 0x10c1f5208>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"history_result = run_history_simulation(num_levers=100, num_selected=5, steps=1000)\n",
"\n",
"print(\"Selected Levers: \")\n",
"for lever in history_result[\"sample\"]:\n",
" print(\"Mu: {0}, Mean Delta: {1:.4f}\".format(lever.mu, \n",
" sum(lever.deltas)/len(lever.deltas)))\n",
"\n",
"display_results(history_result)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Below are the final ten machines and their mean deltas. Although they're not ordered perfectly, this approach still ends up selecting the machine with the highest mean value and lowest delta after enough steps:"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Mu: 91, Mean Delta: -6.0507\n",
"Mu: 92, Mean Delta: -6.7578\n",
"Mu: 93, Mean Delta: -6.0826\n",
"Mu: 94, Mean Delta: -5.6559\n",
"Mu: 95, Mean Delta: -7.0706\n",
"Mu: 96, Mean Delta: -5.7516\n",
"Mu: 97, Mean Delta: -8.1045\n",
"Mu: 98, Mean Delta: -5.6500\n",
"Mu: 99, Mean Delta: -5.6606\n",
"Mu: 100, Mean Delta: -5.6185\n"
]
}
],
"source": [
"for lever in history_result[\"levers\"][-10:]:\n",
" print(\"Mu: {0}, Mean Delta: {1:.4f}\".format(lever.mu, \n",
" sum(lever.deltas)/len(lever.deltas)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Conclusion\n",
"\n",
"In reality, the random noise in situations like these could be much, much larger, which might prevent an approach like this from converging. In addition, society often makes many changes at once that can affect multiple future time steps, so it would be hard to associate score changes with a single machine. But this solution is a start so maybe I can try to address these additional complications in the future. "
]
}
],
"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": 2
}
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