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<li class="toctree-l2"><a class="reference internal" href="#the-approach">The Approach</a></li>
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<div class="section" id="alphazero">
<h1>AlphaZero<a class="headerlink" href="#alphazero" title="Permalink to this headline">¶</a></h1>
<p>A <em>little</em> bit harder problem:</p>
<ul class="simple">
<li>Learn to play complex games given <em>only</em> the rules to the game</li>
<li>Beat the best human players <em>and</em> their best hand-written programs</li>
<li>Learning time limit: Less than a day</li>
</ul>
<img alt="_images/chess_shogi_go.png" src="_images/chess_shogi_go.png" />
<p>Typical result:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Game</span> <span class="mi">3</span> <span class="o">-</span> <span class="n">White</span><span class="p">:</span> <span class="n">AlphaZero</span> <span class="n">Black</span><span class="p">:</span> <span class="n">Stockfish</span>
<span class="mf">1.</span> <span class="n">d4</span> <span class="n">Nf6</span> <span class="mf">2.</span> <span class="n">c4</span> <span class="n">e6</span> <span class="mf">3.</span> <span class="n">Nf3</span> <span class="n">b6</span> <span class="mf">4.</span> <span class="n">g3</span> <span class="n">Bb7</span> <span class="mf">5.</span> <span class="n">Bg2</span> <span class="n">Bb4</span><span class="o">+</span> <span class="mf">6.</span> <span class="n">Bd2</span> <span class="n">Be7</span> <span class="mf">7.</span> <span class="n">Nc3</span> <span class="n">O</span><span class="o">-</span><span class="n">O</span>
<span class="mf">8.</span> <span class="n">Qc2</span> <span class="n">Na6</span> <span class="mf">9.</span> <span class="n">a3</span> <span class="n">c5</span> <span class="mf">10.</span> <span class="n">d5</span> <span class="n">exd5</span> <span class="mf">11.</span> <span class="n">Ng5</span> <span class="n">Nc7</span> <span class="mf">12.</span> <span class="n">h4</span> <span class="n">h6</span> <span class="mf">13.</span> <span class="n">Nxd5</span> <span class="n">Ncxd5</span>
<span class="mf">14.</span> <span class="n">cxd5</span> <span class="n">d6</span> <span class="mf">15.</span> <span class="n">a4</span> <span class="n">Qd7</span> <span class="mf">16.</span> <span class="n">Bc3</span> <span class="n">Rfe8</span> <span class="mf">17.</span> <span class="n">O</span><span class="o">-</span><span class="n">O</span><span class="o">-</span><span class="n">O</span> <span class="n">Bd8</span> <span class="mf">18.</span> <span class="n">e4</span> <span class="n">Ng4</span>
<span class="mf">19.</span> <span class="n">Bh3</span> <span class="n">hxg5</span> <span class="mf">20.</span> <span class="n">f3</span> <span class="n">f5</span> <span class="mf">21.</span> <span class="n">fxg4</span> <span class="n">fxg4</span> <span class="mf">22.</span> <span class="n">Bf1</span> <span class="n">gxh4</span> <span class="mf">23.</span> <span class="n">Bb5</span> <span class="n">Qf7</span>
<span class="mf">24.</span> <span class="n">gxh4</span> <span class="n">Bf6</span> <span class="mf">25.</span> <span class="n">Rhf1</span> <span class="n">Rf8</span> <span class="mf">26.</span> <span class="n">Bxf6</span> <span class="n">gxf6</span> <span class="mf">27.</span> <span class="n">Rf4</span> <span class="n">Qg7</span> <span class="mf">28.</span> <span class="n">Be2</span> <span class="n">Qh6</span>
<span class="mf">29.</span> <span class="n">Rdf1</span> <span class="n">g3</span> <span class="mf">30.</span> <span class="n">Qd3</span> <span class="n">Kh8</span> <span class="mf">31.</span> <span class="n">Qxg3</span> <span class="n">Rae8</span> <span class="mf">32.</span> <span class="n">Bd3</span> <span class="n">Bc8</span> <span class="mf">33.</span> <span class="n">Kb1</span> <span class="n">Rf7</span>
<span class="mf">34.</span> <span class="n">Qf2</span> <span class="n">Bd7</span> <span class="mf">35.</span> <span class="n">h5</span> <span class="n">Ref8</span> <span class="mf">36.</span> <span class="n">Bc2</span> <span class="n">Be8</span> <span class="mf">37.</span> <span class="n">Rf3</span> <span class="n">Re7</span> <span class="mf">38.</span> <span class="n">Rxf6</span> <span class="n">Qxf6</span>
<span class="mf">39.</span> <span class="n">Qxf6</span><span class="o">+</span> <span class="n">Rxf6</span> <span class="mf">40.</span> <span class="n">Rxf6</span> <span class="n">Kg7</span> <span class="mf">41.</span> <span class="n">Rxd6</span> <span class="n">Bxh5</span> <span class="mf">42.</span> <span class="n">Kc1</span> <span class="n">Re5</span> <span class="mf">43.</span> <span class="n">a5</span> <span class="n">bxa5</span>
<span class="mf">44.</span> <span class="n">Kd2</span> <span class="n">Be8</span> <span class="mf">45.</span> <span class="n">Ra6</span> <span class="n">Rh5</span> <span class="mf">46.</span> <span class="n">Bd3</span> <span class="n">a4</span> <span class="mf">47.</span> <span class="n">d6</span> <span class="n">Bf7</span> <span class="mf">48.</span> <span class="n">d7</span> <span class="n">Rh8</span> <span class="mf">49.</span> <span class="n">e5</span> <span class="mi">1</span><span class="o">-</span><span class="mi">0</span>
</pre></div>
</div>
<div class="section" id="the-approach">
<h2>The Approach<a class="headerlink" href="#the-approach" title="Permalink to this headline">¶</a></h2>
<ol class="arabic simple">
<li>MCTS – Monte Carlo Tree Search</li>
<li>Reinforcment Learning</li>
<li>Deep convolutional neural networks</li>
</ol>
<p>The DeepMind team published their results five months ago in the
December 2018 <em>Science</em>, “A general reinforcement learning
algorithm that masters chess, shogi and Go through self-play”.
See: <a class="reference external" href="https://deepmind.com/documents/260/alphazero_preprint.pdf">https://deepmind.com/documents/260/alphazero_preprint.pdf</a></p>
<p>Their self-assessment:</p>
<blockquote>
<div>“Our results demonstrate that a general-purpose reinforcement learning algorithm
can learn, tabula rasa – without domain-specific human knowledge or data, as
evidenced by the same algorithm succeeding in multiple domains – superhuman
performance across multiple challenging games.”</div></blockquote>
<p>Assessment by Garry Kasparov:</p>
<blockquote>
<div>“I can’t disguise my satisfaction that it plays with a very dynamic style, much like my own!”</div></blockquote>
</div>
<div class="section" id="code-you-can-run">
<h2>Code You Can Run<a class="headerlink" href="#code-you-can-run" title="Permalink to this headline">¶</a></h2>
<p>The advancements from <em>AlphaZero</em> were incorporated in incorporated <em>Leela Chess
Zero</em></p>
<p>Leela Chess is free software. See <a class="reference external" href="https://github.com/LeelaChessZero/lc0">https://github.com/LeelaChessZero/lc0</a></p>
<p>It is built using <em>Meson</em> with Python 3 but running primary CUDA code on the
GPU.</p>
<p>See the <a class="reference external" href="http://blog.lczero.org/2018/12/alphazero-paper-and-lc0-v0191.html">LCBlog blog</a> to get started.</p>
</div>
<div class="section" id="overview-of-monte-carlo-tree-search">
<h2>Overview of Monte Carlo Tree Search<a class="headerlink" href="#overview-of-monte-carlo-tree-search" title="Permalink to this headline">¶</a></h2>
<img alt="_images/MCTS_(English)_-_Updated_2017-11-19.svg" src="_images/MCTS_(English)_-_Updated_2017-11-19.svg" /></div>
<div class="section" id="the-algorithm">
<h2>The Algorithm<a class="headerlink" href="#the-algorithm" title="Permalink to this headline">¶</a></h2>
<p>Here is the outline as summarized in the DeepMind paper:</p>
<blockquote>
<div><p>AlphaZero replaces the handcrafted knowledge and domain-specific augmentations
used in traditional game-playing programs with deep neural networks, a
general-purpose reinforcement learning algorithm, and a general-purpose tree
search algorithm.</p>
<p>Instead of a handcrafted evaluation function and move ordering heuristics,
AlphaZero uses a deep neural network (p, v) = fθ(s) with parameters θ. This
neural network fθ(s) takes the board position s as an input and outputs a vector
of move probabilities p with components pa = Pr(a|s) for each action a, and a
scalar value v estimating the expected outcome z of the game from position s, v
≈ E[z|s]. AlphaZero learns these move probabilities and value estimates entirely
from self-play; these are then used to guide its search in future games.</p>
<p>Instead of an alpha-beta search with domain-specific enhancements, AlphaZero
uses a generalpurpose Monte Carlo tree search (MCTS) algorithm. Each search
consists of a series of simulated games of self-play that traverse a tree from
root state sroot until a leaf state is reached. Each simulation proceeds by
selecting in each state s a move a with low visit count (not previously
frequently explored), high move probability and high value (averaged over the
leaf states of simulations that selected a from s) according to the current
neural network fθ. The search returns a vector π representing a probability
distribution over moves, πa = Pr(a|sroot).</p>
<p>The parameters θ of the deep neural network in AlphaZero are trained by
reinforcement learning from self-play games, starting from randomly
initialized parameters θ. Each game is played by running an MCTS search
from the current position sroot = st at turn t, and then selecting a move,
at ∼ πt , either proportionally (for exploration) or greedily (for
exploitation) with respect to the visit counts at the root state. At the
end of the game, the terminal position sT is scored according to the rules
of the game to compute the game outcome z: −1 for a loss, 0 for a draw,
and +1 for a win. The neural network parameters θ are updated to minimize
the error between the predicted outcome vt and the game outcome z, and to
maximize the similarity of the policy vector pt to the search
probabilities πt. The updated parameters are used in subsequent games of
self-play.</p>
</div></blockquote>
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