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<li class="toctree-l2"><a class="reference internal" href="#example-of-simulation-configuration">Example of simulation configuration</a></li>
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<div class="section" id="structure-and-sparsity-of-stochastic-multi-armed-bandits">
<h1><strong>Structure and Sparsity of Stochastic Multi-Armed Bandits</strong><a class="headerlink" href="#structure-and-sparsity-of-stochastic-multi-armed-bandits" title="Permalink to this headline">¶</a></h1>
<p>This page explains shortly what I studied on sparse stochastic multi-armed bandits.
Assume a MAB problem with <code class="docutils literal notranslate"><span class="pre">$K$</span></code> arms, each parametrized by its <em>mean</em> <code class="docutils literal notranslate"><span class="pre">$\mu_k\in\mathbb{R}$</span></code>.
If you know in advance that only a small subset (of size <code class="docutils literal notranslate"><span class="pre">$s$</span></code>) of the arms have a positive arm, it sounds reasonable to hope to be more efficient in playing the bandit game compared to an approach which is non aware of the sparsity.</p>
<p>The <a class="reference external" href="docs/Policies.SparseUCB.html#Policies.SparseUCB.SparseUCB"><code class="docutils literal notranslate"><span class="pre">SparseUCB</span></code></a> is an extension of the well-known <a class="reference external" href="docs/Policies.UCB.html"><code class="docutils literal notranslate"><span class="pre">UCB</span></code></a>, and requires to known <strong>exactly</strong> the value of <code class="docutils literal notranslate"><span class="pre">$s$</span></code>.
It works by identifying as fast as possible (actually, in a sub-logarithmic number of samples) the arms with non-positive means.
Then it only plays in the “good” arms with positive means, with a regular UCB policy.</p>
<p>I studied extensions of this idea, first of all the <a class="reference external" href="docs/Policies.SparseklUCB.html#Policies.SparseklUCB.SparseklUCB"><code class="docutils literal notranslate"><span class="pre">SparseklUCB</span></code></a> policy as it was suggested in the original research paper, but mainly a generic “wrapper” black-box approach.
For more details, see <a class="reference external" href="docs/Policies.SparseWrapper.html#Policies.SparseWrapper.SparseWrapper"><code class="docutils literal notranslate"><span class="pre">SparseWrapper</span></code></a>.</p>
<ul class="simple">
<li><p>Reference: [<a class="reference external" href="https://arxiv.org/abs/1706.01383">“Sparse Stochastic Bandits”, by J. Kwon, V. Perchet & C. Vernade, COLT 2017</a>]. Note that this algorithm only works for sparse <a class="reference external" href="(docs/Arms.Gaussian.html)">Gaussian</a> (or sub-Gaussian) stochastic bandits, and it includes <a class="reference external" href="docs/Arms.Bernoulli.html">Bernoulli arms</a>.</p></li>
</ul>
<hr class="docutils" />
<div class="section" id="article">
<h2>Article<a class="headerlink" href="#article" title="Permalink to this headline">¶</a></h2>
<blockquote>
<div><p>TODO finish! I am writing a small research article on that topic, it is a better introduction as a self-contained document to explain this idea and the algorithms. Reference: <a class="reference external" href="https://hal.inria.fr/hal-XXX">[Structure and Sparsity of Stochastic Multi-Arm Bandits, Lilian Besson and Emilie Kaufmann, 2018]</a>.</p>
</div></blockquote>
</div>
<hr class="docutils" />
<div class="section" id="example-of-simulation-configuration">
<h2>Example of simulation configuration<a class="headerlink" href="#example-of-simulation-configuration" title="Permalink to this headline">¶</a></h2>
<p>A simple python file, <a class="reference external" href="https://smpybandits.github.io/docs/configuration_sparse.html"><code class="docutils literal notranslate"><span class="pre">configuration_sparse.py</span></code></a>, is used to import the <a class="reference external" href="Arms/">arm classes</a>, the <a class="reference external" href="Policies/">policy classes</a> and define the problems and the experiments.</p>
<p>For example, we can compare the standard <a class="reference external" href="docs/Policies.UCB.html"><code class="docutils literal notranslate"><span class="pre">UCB</span></code></a> and <a class="reference external" href="docs/Policies.BayesUCB.html"><code class="docutils literal notranslate"><span class="pre">BayesUCB</span></code></a> algorithms, non aware of the sparsity, against the sparsity-aware <a class="reference external" href="docs/Policies.SparseUCB.html"><code class="docutils literal notranslate"><span class="pre">SparseUCB</span></code></a> algorithm, as well as 4 versions of <a class="reference external" href="docs/Policies.SparseWrapper.html"><code class="docutils literal notranslate"><span class="pre">SparseWrapper</span></code></a> applied to <a class="reference external" href="docs/Policies.BayesUCB.html"><code class="docutils literal notranslate"><span class="pre">BayesUCB</span></code></a>.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">configuration</span> <span class="o">=</span> <span class="p">{</span>
<span class="s2">"horizon"</span><span class="p">:</span> <span class="mi">10000</span><span class="p">,</span> <span class="c1"># Finite horizon of the simulation</span>
<span class="s2">"repetitions"</span><span class="p">:</span> <span class="mi">100</span><span class="p">,</span> <span class="c1"># number of repetitions</span>
<span class="s2">"n_jobs"</span><span class="p">:</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="c1"># Maximum number of cores for parallelization: use ALL your CPU</span>
<span class="s2">"verbosity"</span><span class="p">:</span> <span class="mi">5</span><span class="p">,</span> <span class="c1"># Verbosity for the joblib calls</span>
<span class="c1"># Environment configuration, you can set up more than one.</span>
<span class="s2">"environment"</span><span class="p">:</span> <span class="p">[</span>
<span class="p">{</span> <span class="c1"># sparsity = nb of >= 0 mean, = 3 here</span>
<span class="s2">"arm_type"</span><span class="p">:</span> <span class="n">Bernoulli</span><span class="p">,</span>
<span class="s2">"params"</span><span class="p">:</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.2</span><span class="p">,</span> <span class="mf">0.3</span>
<span class="p">}</span>
<span class="p">],</span>
<span class="c1"># Policies that should be simulated, and their parameters.</span>
<span class="s2">"policies"</span><span class="p">:</span> <span class="p">[</span>
<span class="p">{</span><span class="s2">"archtype"</span><span class="p">:</span> <span class="n">UCB</span><span class="p">,</span> <span class="s2">"params"</span><span class="p">:</span> <span class="p">{}</span> <span class="p">},</span>
<span class="p">{</span><span class="s2">"archtype"</span><span class="p">:</span> <span class="n">SparseUCB</span><span class="p">,</span> <span class="s2">"params"</span><span class="p">:</span> <span class="p">{</span> <span class="s2">"sparsity"</span><span class="p">:</span> <span class="mi">3</span> <span class="p">}</span> <span class="p">},</span>
<span class="p">{</span><span class="s2">"archtype"</span><span class="p">:</span> <span class="n">BayesUCB</span><span class="p">,</span> <span class="s2">"params"</span><span class="p">:</span> <span class="p">{</span> <span class="p">}</span> <span class="p">},</span>
<span class="p">]</span>
<span class="p">}</span>
</pre></div>
</div>
<p>Then add a <a class="reference external" href="docs/Policies.SparseWrapper.html">Sparse-Wrapper</a> bandit algorithm (<a class="reference external" href="docs/Policies.SparseWrapper.html"><code class="docutils literal notranslate"><span class="pre">SparseWrapper</span></code> class</a>), you can use this piece of code:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">configuration</span><span class="p">[</span><span class="s2">"policies"</span><span class="p">]</span> <span class="o">+=</span> <span class="p">[</span>
<span class="p">{</span>
<span class="s2">"archtype"</span><span class="p">:</span> <span class="n">SparseWrapper</span><span class="p">,</span>
<span class="s2">"params"</span><span class="p">:</span> <span class="p">{</span>
<span class="s2">"policy"</span><span class="p">:</span> <span class="n">BayesUCB</span><span class="p">,</span>
<span class="s2">"use_ucb_for_set_J"</span><span class="p">:</span> <span class="n">use_ucb_for_set_J</span><span class="p">,</span>
<span class="s2">"use_ucb_for_set_K"</span><span class="p">:</span> <span class="n">use_ucb_for_set_K</span><span class="p">,</span>
<span class="p">}</span>
<span class="p">}</span>
<span class="k">for</span> <span class="n">use_ucb_for_set_J</span> <span class="ow">in</span> <span class="p">[</span> <span class="bp">True</span><span class="p">,</span> <span class="bp">False</span> <span class="p">]</span>
<span class="k">for</span> <span class="n">use_ucb_for_set_K</span> <span class="ow">in</span> <span class="p">[</span> <span class="bp">True</span><span class="p">,</span> <span class="bp">False</span> <span class="p">]</span>
<span class="p">]</span>
</pre></div>
</div>
</div>
<hr class="docutils" />
<div class="section" id="how-to-run-the-experiments">
<h2><a class="reference internal" href="How_to_run_the_code.html"><span class="doc">How to run the experiments ?</span></a><a class="headerlink" href="#how-to-run-the-experiments" title="Permalink to this headline">¶</a></h2>
<p>You should use the provided <a class="reference external" href="Makefile"><code class="docutils literal notranslate"><span class="pre">Makefile</span></code></a> file to do this simply:</p>
<div class="highlight-bash notranslate"><div class="highlight"><pre><span></span>make install <span class="c1"># install the requirements ONLY ONCE</span>
make sparse <span class="c1"># run and log the main.py script</span>
</pre></div>
</div>
</div>
<hr class="docutils" />
<div class="section" id="some-illustrations">
<h2>Some illustrations<a class="headerlink" href="#some-illustrations" title="Permalink to this headline">¶</a></h2>
<p>Here are some plots illustrating the performances of the different <a class="reference external" href="docs/Policies.">policies</a> implemented in this project, against various sparse problems (with <a class="reference external" href="Arms/Bernoulli.html"><code class="docutils literal notranslate"><span class="pre">Bernoulli</span></code></a> or <a class="reference external" href="https://smpybandits.github.io/docs/Arms.Gaussian.html"><code class="docutils literal notranslate"><span class="pre">UnboundedGaussian</span></code></a> arms only):</p>
<div class="section" id="variants-of-sparse-wrapper-for-ucb-on-a-simple-sparse-bernoulli-problem">
<h3>3 variants of <a class="reference external" href="docs/Policies.SparseWrapper.html">Sparse-Wrapper</a> for UCB, on a “simple” sparse Bernoulli problem<a class="headerlink" href="#variants-of-sparse-wrapper-for-ucb-on-a-simple-sparse-bernoulli-problem" title="Permalink to this headline">¶</a></h3>
<p><img alt="3 variants of Sparse-Wrapper for UCB, on a "simple" sparse Bernoulli problem" src="plots/main____env1-1_XXX.png" /></p>
<p>FIXME run some simulations and explain them!</p>
<blockquote>
<div><p>These illustrations come from my (work in progress) article, <a class="reference external" href="https://hal.inria.fr/hal-XXX">[Structure and Sparsity of Stochastic Multi-Arm Bandits, Lilian Besson and Emilie Kaufmann, 2018]</a>.</p>
</div></blockquote>
</div>
<hr class="docutils" />
<div class="section" id="scroll-license-github-license">
<h3>📜 License ? <a class="reference external" href="https://github.com/SMPyBandits/SMPyBandits/blob/master/LICENSE"><img alt="GitHub license" src="https://img.shields.io/github/license/SMPyBandits/SMPyBandits.svg" /></a><a class="headerlink" href="#scroll-license-github-license" title="Permalink to this headline">¶</a></h3>
<p><a class="reference external" href="https://lbesson.mit-license.org/">MIT Licensed</a> (file <a class="reference external" href="LICENSE">LICENSE</a>).</p>
<p>© 2016-2018 <a class="reference external" href="https://GitHub.com/Naereen">Lilian Besson</a>.</p>
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