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Specialised table CSS. Added bandits demo.

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1 parent 9716bbd commit 86e40ea0f08e5accd1e97595aef1121e83d82506 Mark Reid committed Apr 6, 2010
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69 code/bandits/index.md
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+---
+layout: name
+section: Code
+title: Bandits Demo
+---
+
+Multi-armed Bandit Demo
+=======================
+
+This is a simple JavaScript demonstration of some algorithms for the multi-armed
+bandit problem.
+
+Some background, references, and information about the bandit problem can be found at
+my [GitHub](http://github.com/mreid/Bandits/) repository, along with the source code.
+
+<table id="controls" style="border: 1px solid gray;padding: 1ex;width:100%;">
+ <tr style="text-align:left;">
+ <th>Bandits</th>
+ <th>Agents</th>
+ </tr>
+ <tr>
+ <td style="vertical-align: top; width: 40%;">
+ <ol id="bandit"></ol>
+ </td>
+
+ <td style="vertical-align: top; width: 40%;">
+ <ol id="agent"></ol>
+ </td>
+ <td style="vertical-align: top;">
+ Run game for
+ <input id="steps" type="text" value="500" size="4"/>
+ <label for="steps">steps</label>.<br/>
+ <button id="run">Go!</button><br/>
+ <label for="average">Average</label>:
+ <input id="average" type="checkbox" checked="true" />
+ </td>
+ </tr>
+</table>
+
+<div id="placeholder" style="margin:0 auto;width:600px;height:300px;text-align:center;border: 1px solid gray;">
+</div>
+
+Running the Demo
+----------------
+Bandits and agents can
+be chosen using the drop-down selections. New bandits and agents can be added by
+clicking the "+ create" link. If a bandit or agent requires parameters these can
+be added in the text areas which appear next to the drop-down menu.
+
+Once the bandits and agents are selected, the number of steps for the game can
+be entered in the text field on the right. Then hit "Go!" to run the game.
+
+The results are plotted below the UI. Rewards for bandits are drawn in light
+grey, agents are in colour and are listed in the plot's legend. (The "Averages"
+check box determines whether running totals or averages are displayed).
+
+<script src="js/lib/jquery.js" type="text/javascript"></script>
+<script src="js/lib/jquery.flot.min.js" type="text/javascript"></script>
+<script src="js/bandits.js" type="text/javascript"></script>
+<script src="js/agents.js" type="text/javascript"></script>
+<script src="js/ui.js" type="text/javascript"></script>
+
+<script type="text/javascript">
+$(document).ready(function(){
+ $('ol #bandit').replaceWith(makeList(banditTypes));
+ $('ol #agent').replaceWith(makeList(agentTypes));
+ $("#run").click(runGame);
+});
+</script>
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261 code/bandits/js/agents.js
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+/**
+ * agents.js
+ * Mark Reid <mark.reid@gmail.com>
+ * Created: 2010-04-05
+ *
+ * Defines a number of agents for playing bandit games within the Agent
+ * namespace.
+ */
+
+// Some simple utility functions
+function sum(array) {
+ var result = 0;
+ for(var i=0 ; i < array.length ; i++) { result += array[i] }
+ return result;
+}
+
+function max(array) {
+ var result = Number.NEGATIVE_INFINITY;
+ for(var i=0 ; i < array.length ; i++) {
+ result = Math.max(result,array[i]);
+ }
+ return result;
+}
+
+function draw(probs) {
+ var x = Math.random();
+ var cdf = 0;
+ var selected = 0;
+ while(x > cdf) { cdf += probs[selected++]; }
+ return selected-1;
+}
+
+/**
+ * All agents must provide the following functions/fields:
+ * name: A short string description of the agent.
+ * init(k): Initialise the agent for a k bandit problem.
+ * predict(): Return an index between 0...k-1 as a prediction.
+ * update(r): Update the agent with reward r.
+ * rewards: An array of rewards to date.
+ * predictions: An array of predictions to date.
+ */
+var Agent = {
+ /**
+ * The constant prediction algorithm.
+ * Always chooses bandit with index `i`.
+ */
+ Constant: function(i) {
+ var index = i;
+
+ return {
+ name: 'Constant('+i+')',
+ init: function(num_bandits) { },
+ predict: function() {
+ this.predictions.push(index);
+ return index;
+ },
+ update: function(reward) { this.rewards.push(reward); },
+ rewards: [],
+ predictions: []
+ }
+ },
+
+ /**
+ * An implementation of the UCB1 algorithm from:
+ * P. Auer, N. Cesa-Bianchi, and P. Fischer.
+ * "Finite-time Analysis of the Multiarmed Bandit Problem."
+ * Machine Learning, 47, 235-236, 2002.
+ */
+ UCB1: function() {
+ var k = 0;
+ var played = [];
+ var totals = [];
+ var last = 0;
+
+ function score(i,steps) {
+ var xbar = totals[i]/played[i];
+ var bound = Math.sqrt((2*Math.log(sum(played)))/played[i]);
+
+ return xbar + bound;
+ }
+
+ return {
+ name: "UCB1",
+ init: function(num_bandits) { k = num_bandits; },
+ predict: function() {
+ var p = 0;
+ var steps = this.predictions.length;
+
+ if(played.length < k) {
+ p = played.length;
+ played[p] = 1;
+ } else {
+ for(var i=0 ; i<k ; i++) {
+ if(score(i,steps) > score(p,steps)) p = i;
+ }
+ played[p] += 1;
+ }
+
+ this.predictions.push(p);
+ last = p;
+ return p;
+ },
+ update: function(reward) {
+ this.rewards.push(reward);
+ if(totals.length < k) totals[last] = 0;
+ totals[last] += reward;
+ },
+ rewards: [],
+ predictions: []
+ }
+ },
+
+ /**
+ * An implementation of the Exp3 algorithm from:
+ * P. Auer, N. Cesa-Bianchi, Y. Freund, and R. Schapire.
+ * "The nonstochastic multiarmed bandit problem."
+ * SIAM Journal on Computing, 32(1):48–77, 2002.
+ *
+ * Returns an Exp3 algorithm initialised with input parameter gamma in (0,1].
+ */
+ Exp3: function(gamma) {
+ var exp3 = Agent.Exp3S(gamma,0);
+ exp3.name = "Exp3("+gamma+")";
+ return exp3;
+ },
+
+ /**
+ * An implementation of the Exp3.S algorithm from:
+ * P. Auer, N. Cesa-Bianchi, Y. Freund, and R. Schapire.
+ * "The nonstochastic multiarmed bandit problem."
+ * SIAM Journal on Computing, 32(1):48–77, 2002.
+ *
+ * Returns an Exp3.S algorithm initialised with input parameter
+ * gamma in (0,1] and alpha >= 0.
+ *
+ * Note that when alpha = 0, this algorithm reduces to the original Exp3.
+ */
+ Exp3S: function(gamma,alpha) {
+ var gamma = gamma;
+ var alpha = alpha;
+ var weights = [[]];
+ var k = 0;
+
+ return {
+ name: "Exp3.S("+gamma+","+alpha+")",
+ init: function(num_bandits) {
+ k = num_bandits;
+ for(var i=0 ; i<k ; i++) { weights[0][i] = 1 }
+ },
+ predict: function() {
+ var p = draw(this.probs());
+ this.predictions.push(p);
+ return p;
+ },
+ update: function(reward) {
+ this.rewards.push(reward);
+ var t1 = weights.length;
+ var ws = weights[t1-1];
+ var c = (Math.E * alpha/k)*sum(ws);
+
+ weights[t1] = [];
+ for(var i=0 ; i<k ; i++) {
+ weights[t1][i] = ws[i];
+ if(i === this.predictions[t1-1]) {
+ var xhat = reward/(this.probs()[i]);
+ weights[t1][i] *= Math.exp((gamma*xhat)/k);
+ }
+ weights[t1][i] += c;
+ }
+ },
+ probs: function() {
+ // Compute a set of probabilities from a set of weights.
+ var ws = weights[weights.length-1];
+ var total = sum(ws);
+ var ps = [];
+ for(var i=0 ; i < k ; i++) {
+ ps[i] = (1-gamma)*(ws[i]/total) + gamma/k;
+ }
+ return ps;
+ },
+ rewards: [],
+ predictions: []
+ }
+ },
+
+ /**
+ * An implementation of the Exp3.1 algorithm from:
+ * P. Auer, N. Cesa-Bianchi, Y. Freund, and R. Schapire.
+ * "The nonstochastic multiarmed bandit problem."
+ * SIAM Journal on Computing, 32(1):48–77, 2002.
+ *
+ * Returns an Exp3.1 agent
+ */
+ Exp31: function() {
+ var k = 0, // Number of bandits
+ r = 0, // Current epoch
+ exp3 = undefined, // Exp3 subroutine
+ totals = [], // The estimated total reward for each bandit
+ epochs = [], // Which timestep each epoch started
+ g = 0, // Guess for bound
+ gamma = 0; // Parameter for Exp3 subroutine
+
+ return {
+ name: "Exp3.1",
+ init: function(num_bandits) {
+ k = num_bandits;
+ for(var i=0 ; i < k ; i++) { totals[i] = 0; }
+ r = 0;
+ g = (k * Math.log(k))/(Math.E-1);
+ gamma = 1;
+ exp3 = Agent.Exp3(gamma);
+ exp3.init(k);
+ },
+ predict: function() {
+ // Update epoch, g and gamma and reset the Exp3 subroutine.
+ if(max(totals) > g - k/gamma) {
+ r += 1; g *= 4; gamma /= 2;
+ epochs.push(this.t());
+ exp3 = Agent.Exp3(gamma);
+ exp3.init(k);
+ }
+ var p = exp3.predict();
+ this.predictions.push(p);
+ return p;
+ },
+ update: function(reward) {
+ this.rewards.push(reward);
+ exp3.update(reward);
+ totals[this.last()] += reward/(exp3.probs()[this.last()]);
+ },
+ t: function() { return this.predictions.length; },
+ last: function() {
+ return this.predictions[this.t()-1];
+ },
+ epochs: function() { return epochs; },
+ rewards: [],
+ predictions: []
+ }
+ },
+
+ /**
+ * The random strategy. Chooses a bandit index from a uniform distribution.
+ */
+ Random: function() {
+ var range = 0;
+
+ return {
+ name: "Random",
+ init: function(num_bandits) { range = num_bandits; },
+ predict: function() {
+ var p = Math.floor(Math.random() * range);
+ this.predictions.push(p);
+ return p;
+ },
+ update: function(reward) { this.rewards.push(reward) },
+ rewards: [],
+ predictions: []
+ }
+ }
+};
+
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63 code/bandits/js/bandits.js
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+/**
+ * Bandits provide the following functions:
+ * name: a short string describing the bandit
+ * reward: a function returning a reward in [0,1]
+ * rewards: an array of rewards returned reward()
+ * total: the current sum of rewards returned by reward()
+ */
+var Bandit = {
+ /**
+ * Construct a bandit that returns a reward of 1 with probability p and
+ * zero otherwise.
+ */
+ Bernoulli: function(p) {
+ var p = p;
+
+ return {
+ name: "Bernoulli("+p+")",
+ reward: function() {
+ var v = 1 && ( Math.random() < p ) || 0 ;
+ this.rewards.push(v);
+ this.total += v;
+ return v;
+ },
+ rewards: [],
+ total: 0
+ }
+ }
+}
+
+/**
+ * A bandit game.
+ * run(steps): Runs the game for the given number of steps.
+ */
+function Game(agents, bandits) {
+ var agents = agents;
+ var bandits = bandits;
+
+ return {
+ run: function(steps) {
+ // Initialise all the agents
+ for(var a=0 ; a<agents.length ; a++) {
+ agents[a].init(bandits.length);
+ }
+
+ // Play the game for the required number of steps
+ for(var t=0 ; t<steps ; t++) {
+
+ // Compute all the rewards
+ var rewards = [];
+ for(var b=0 ; b<bandits.length ; b++) {
+ rewards[b] = bandits[b].reward();
+ }
+
+ // Get the agents' predictions and give rewards
+ for(var a=0 ; a<agents.length ; a++) {
+ var choice = agents[a].predict();
+ var reward = rewards[choice];
+ agents[a].update(reward);
+ }
+ }
+ }
+ }
+}
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154 code/bandits/js/lib/jQuery.js
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+/*!
+ * jQuery JavaScript Library v1.4.2
+ * http://jquery.com/
+ *
+ * Copyright 2010, John Resig
+ * Dual licensed under the MIT or GPL Version 2 licenses.
+ * http://jquery.org/license
+ *
+ * Includes Sizzle.js
+ * http://sizzlejs.com/
+ * Copyright 2010, The Dojo Foundation
+ * Released under the MIT, BSD, and GPL Licenses.
+ *
+ * Date: Sat Feb 13 22:33:48 2010 -0500
+ */
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View
1 code/bandits/js/lib/jquery.flot.min.js
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View
174 code/bandits/js/ui.js
@@ -0,0 +1,174 @@
+function running_totals(rewards) {
+ var totals = [];
+ var reward = 0;
+ for(var t=0 ; t < rewards.length ; t++) {
+ reward += rewards[t];
+ totals.push([t+1,reward]);
+ }
+ return totals;
+}
+
+function running_average(rewards) {
+ var totals = [];
+ var reward = 0;
+ for(var t=0 ; t < rewards.length ; t++) {
+ reward += rewards[t];
+ totals.push([t+1,reward/(t+1)]);
+ }
+ return totals;
+}
+
+function plotRewards(fn, rewards, options) {
+ var plot = { lines: {show: true}, shadowSize: 0, lineWidth: 1 };
+ for(opt in options) { plot[opt] = options[opt]; }
+ plot.data = fn(rewards);
+ return plot;
+}
+
+// Returns plot markings for an agent, if appropriate.
+// Currently, just plots epoch transitions for Exp3.1 in light blue
+function agentMarkings(agent) {
+ var marks = [];
+ if(agent.epochs !== undefined) {
+ var epochs = agent.epochs();
+ for(var e=0 ; e < epochs.length ; e++) {
+ marks.push(
+ { color: '#99f', lineWidth: 1,
+ xaxis: { from: epochs[e], to: epochs[e] }}
+ );
+ }
+ }
+ return marks;
+}
+
+var banditTypes = {
+ name: 'bandit',
+ types: {
+ "Bernoulli": { constructor: Bandit.Bernoulli, args: [ 0.1 ] }
+ },
+ defaults: [
+ [ 'Bernoulli', 0.1 ],
+ [ 'Bernoulli', 0.3 ],
+ [ 'Bernoulli', 0.8 ]
+ ]
+}
+var agentTypes = {
+ name: 'agent',
+ types: {
+ "Random": { constructor: Agent.Random },
+ "UCB1": { constructor: Agent.UCB1 },
+ "Exp3": { constructor: Agent.Exp3, args: [0.1] },
+ "Exp3.1": { constructor: Agent.Exp31 },
+ "Exp3.S": { constructor: Agent.Exp3S, args: [0.1, 0.002] },
+ },
+ defaults: [
+ [ 'Exp3.1' ]
+ ]
+}
+
+function runGame() {
+ var steps = $('#steps').val();
+ var bandits = builder(banditTypes);
+ var agents = builder(agentTypes);
+ var markings = [];
+
+ var fn;
+ var yaxis;
+ if($('#average:checked').val()) {
+ fn = running_average;
+ yaxis = { min: 0, max: 1 };
+ } else {
+ fn = running_totals;
+ }
+
+ Game(agents, bandits).run(steps);
+
+ // Plot agents
+ var plots = [ ];
+ for(var a=0 ; a < agents.length ; a++) {
+ var agent = agents[a];
+ plots.push(plotRewards(fn, agent.rewards, { label: agent.name }));
+ markings = markings.concat(agentMarkings(agents[a]));
+ }
+
+ // Plot bandits
+ var banditColor = 'rgba(127,127,127,0.6)';
+ for(var b=0 ; b < bandits.length ; b++) {
+ var bandit = bandits[b];
+ plots.push(plotRewards(fn, bandit.rewards, {color: banditColor}));
+ }
+
+ // Draw it!
+ $.plot(
+ $("#placeholder"),
+ plots,
+ { // yaxis: { min: 0, max: 1},
+ legend: { position: "se" },
+ yaxis: yaxis,
+ grid: { markings: markings } }
+ );
+}
+
+function builder(kind) {
+ var objs = [];
+ $('.'+kind.name+' select').each(function(i){
+ var constructor = kind.types[$(this).val()].constructor;
+ var args = [];
+ $(this).next('.args').find('input').each(function(j) {
+ args.push($(this).val());
+ });
+ objs.push(constructor.apply(this,args));
+ });
+ return objs;
+}
+
+function makeNew(kind) {
+ return $('<a/>')
+ .text('+ create').attr('href', '')
+ .click(function(event) {
+ event.preventDefault();
+ $(this).before(makeSelector(kind));
+ });
+}
+
+function makeList(kind) {
+ var list = $('ol#'+kind.name);
+ for(var i = 0 ; i < kind.defaults.length ; i++) {
+ var selector = makeSelector(kind);
+ selector.find('select').val(kind.defaults[i][0]);
+ selector.find('input').each(function(j) {
+ $(this).val(kind.defaults[i][j+1]);
+ });
+ list.append(selector);
+ }
+ list.append(makeNew(kind));
+ return list;
+}
+
+function makeSelector(kind) {
+ var li = $("<li/>").addClass(kind.name);
+ var select = $("<select/>");
+ for(type in kind.types) {
+ var option = $('<option/>').attr('label', type);
+ select.append(option);
+ select.change(function(event) {
+ var value = $(this).val();
+ $(this).next('.args').replaceWith(makeArgs(kind,value));
+ });
+ }
+ li.append(select);
+ li.append($('<div/>').addClass('args'));
+ select.change();
+ return li;
+}
+
+function makeArgs(kind,type) {
+ var args = $('<div/>').addClass('args').css('display', 'inline');
+ var properties = kind.types[type];
+ if(properties && properties.args) {
+ properties.args.forEach(function(arg) {
+ args.append('<input type="text" size="5" value="'+arg+'"/>');
+ });
+ }
+ return args;
+}
View
8 code/index.markdown
@@ -12,6 +12,14 @@ Eventually this page will contain links to most of the research and non-research
related programming I've done.
<div class="section" markdown="1">
+Demos
+=====
+[Mutli-armed Bandits](/code/bandits/)
+: This JavaScript demo allows you to configure and run a multi-armed bandit game
+ and plot the resulting rewards for a variety of agents.
+</div>
+
+<div class="section" markdown="1">
Tools
=====
[Feed Bag](/code/feed-bag.html)
View
10 files/css/screen.css
@@ -140,16 +140,16 @@ blockquote {
border-bottom: 1px solid silver;
}
/* @group Table */
-table {
+table.neat {
width: 80%;
margin: 1.5em auto 1.5em auto;
table-layout: fixed;
border-spacing: 0;
}
-table tr { text-align: center; }
-table th { font-weight: normal; background-color: #eeeeee; }
-table td { background-color: white; }
-table th.title { border-bottom: 1px solid gray; border-top: 1px solid gray; vertical-align: bottom; background-color: lightgrey; }
+table.neat tr { text-align: center; }
+table.neat th { font-weight: normal; background-color: #eeeeee; }
+table.neat td { background-color: white; }
+table.neat th.title { border-bottom: 1px solid gray; border-top: 1px solid gray; vertical-align: bottom; background-color: lightgrey; }
caption {
color: #333;
font-size: 0.875em;
View
4 iem/_posts/2008-06-17-visualising-19th-century-reading.markdown
@@ -33,7 +33,7 @@ After an initial inspection, my first thought was to try to visualise the simila
The full database contains 99,692 loans of 7,078 different books from 11 libraries by one of the 2,642 people. To make this more manageable, I focused on books that had at least 20 different borrowers and only considered people who had borrowed one of these books.
This distilled the database down to a simple table with each row representing one of 1,616 books and each column representing one of 2,473 people.
-<table>
+<table class="neat">
<caption>Table 1: A portion of the book and borrower table. A 1 indicates that the borrower (column)
borrowed the book (row) at least once. A 0 indicates that the borrower never borrowed the book.
</caption>
@@ -75,7 +75,7 @@ A standard technique for doing this is [Principal Component Analysis][pca]. Intu
[pca]: http://en.wikipedia.org/wiki/Principal_components_analysis
-<table>
+<table class="neat">
<caption>Table 2: A portion of the book table after PCA. The values in the two new columns (PCA IDs) can be used to plot the books.
</caption>
<tr><th rowspan="2" class="title">Book<br/>ID</th><th colspan="2" class="title">PCA ID</th></tr>

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