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<a class="post-title-link" href="/2018/11/18/强化学习漫谈-14-Multi-Agent-2/" itemprop="url">强化学习漫谈 14：Multi Agent RL 之二</a></h1>
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<span id="/2018/11/18/强化学习漫谈-14-Multi-Agent-2/" class="leancloud_visitors" data-flag-title="强化学习漫谈 14：Multi Agent RL 之二">
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<p>本节介绍<strong>去中心化策略的集中式学习</strong>(Centralized Learning of Decentralized Policies)这一类算法，具体会介绍三种算法：RLAR，COMA，QMIX。</p>
<p>这类算法的主要想法是：训练过程是离线的，所以可以有环境状态与joint action的全局观测(fully observation)；而执行过程是在线的，各个agent独自按照学习的策略进行每一步动作，策略不是状态$s$的函数，而是<strong>action-observation history </strong> $\mathcal{H}_{i,t}$的函数。<br>
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<a class="post-title-link" href="/2018/11/18/强化学习漫谈-13-Multi-Agent-1/" itemprop="url">强化学习漫谈 13：Multi Agent RL 之一</a></h1>
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<p>前面介绍了强化学习大致的理论框架和实际使用的一些方法，这个体系都是围绕着agent对environment进行观察、动作、得到反馈这样的交互方式来进行的。我们把这个问题的适用范围进一步扩大，如果有多个agent同时对environment进行观察、动作、得到反馈；如果这多个agent或者互相协助，或者互相竞争，或者互相博弈；如果这些agent对环境本身没有全貌的观察；如果每个agent的Q value受到其他agent的影响；… …；我们应该有什么样的理论框架和实际方法？我们面临什么样的机会和挑战？下面就从理论框架和实际方法两个方面介绍Multi-Agent（多智体）的强化学习。</p>
<h3 id="理论框架：Stochastic-Game-SG-与-Dec-POMDP"><a href="#理论框架：Stochastic-Game-SG-与-Dec-POMDP" class="headerlink" title="理论框架：Stochastic Game (SG) 与 Dec-POMDP"></a>理论框架：Stochastic Game (SG) 与 Dec-POMDP</h3>
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<p>Going Deep。DQN<a href="https://arxiv.org/abs/1312.5602" target="_blank" rel="noopener">论文1</a>、<a href="https://www.nature.com/articles/nature14236" target="_blank" rel="noopener">论文2</a>; DDPG<a href="https://arxiv.org/abs/1509.02971" target="_blank" rel="noopener">论文</a>；A3C<a href="https://arxiv.org/abs/1602.01783" target="_blank" rel="noopener">论文</a>。</p>
<h3 id="DQN：Deep-Q-Learning"><a href="#DQN：Deep-Q-Learning" class="headerlink" title="DQN：Deep Q Learning"></a>DQN：Deep Q Learning</h3><p>在Function Approximation中，我们希望得到的是模型的表达能力和泛化能力；另一方面，当状态数据来自于图像、视频、声音等原始数据时，我们也希望增强模型的特征提取能力，减少人工特征工程。因此运用深度学习对强化学习中的value function、policy function进行端到端的approximation，成为一个有趣的选项。</p>
<p>然而不做任何trick地直接应用深度学习，存在如下问题：</p>
<ol>
<li>强化学习中的return计算通常相对当前的time step而言有延迟，即使是Bootstrapping，也会有n-step的延迟。</li>
<li>深度学习的训练样本需要独立同分布i.i.d，而强化学习的状态、回报等都有很强的前后相关性。</li>
<li>深度学习适用于数据的概率分布是平稳(stationary)的情况，而强化学习中，策略提升(policy improvement)会带来状态分布的变化，有时候在参数BP的过程中，策略参数$\theta$的变化会带来状态分布的很大的变化，从而使训练过程震荡或者diverge。</li>
</ol>
<p>因此上面提到的两篇论文针对上面这三个问题，提出了实际工程实现时的一些办法：<br>
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<p>从随机策略到确定性策略，迈向了高维以致连续action空间的方法。<a href="http://www0.cs.ucl.ac.uk/staff/d.silver/web/Publications_files/deterministic-policy-gradients.pdf" target="_blank" rel="noopener">论文</a></p>
<h3 id="关于确定性策略梯度的疑问"><a href="#关于确定性策略梯度的疑问" class="headerlink" title="关于确定性策略梯度的疑问"></a>关于确定性策略梯度的疑问</h3><p>一个非常直观的猜想是，承接上一节的Policy Gredient方法，策略分布函数$\pi(a|s)$有一个初始分布，例如说正态分布$\mathcal{N}(a,\sigma)$，然后我们通过Actor-Critic或者别的方法对这个策略进行逐渐优化，最终收敛到最优策略$\pi^\ast$，这个过程中策略分布函数应该逐步向最优策略演化，并且最优策略直观上应该是方差很小，聚焦于某个或某段确定的值，极端情况下收敛到确定的点成为确定策略。这种情况下最优策略分布集中的区域其方差通常很小（或者说概率函数很<em>陡峭</em>），因此无论$\nabla_\theta\pi(a|s,\theta)$还是$\nabla_\theta\ln\pi(a|s,\theta)$都很大，造成训练过程不稳定（参考一下狄拉克函数求导？）。因此上一节的Policy Gradient Theorem是不能推广到确定性策略梯度方法的。幸运的是，论文中的Deterministic Policy Gradient Theorem给出了确定策略梯度在理论上的支撑。<br>
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<p>Value Function可以用参数化来回归，Policy $\pi(a|s)$ 能否也用参数化回归/拟合？如何通过梯度方法寻找最优策略？相比$\epsilon$-greedy的优点在哪里？</p>
<h3 id="参数化拟合Policy-pi-a-s"><a href="#参数化拟合Policy-pi-a-s" class="headerlink" title="参数化拟合Policy $\pi(a|s)$"></a>参数化拟合Policy $\pi(a|s)$</h3><p>从前两章得到启发，既然值函数$v(s)$或者action value $q(s,a)$可以用函数来拟合，通过调整参数$w$来学习，我们是否也可以将策略$\pi(a|s)$用函数来拟合，通过调整参数$\theta$来寻找最优策略？策略拟合函数表达为$\pi(a|s,\theta)$，例如，对于离散化action，该函数可以用exponential softmax表达为：<br>\begin{equation}<br>\pi(a|s,\theta)=\frac{\exp(h(s,a,\theta))}{\sum_b\exp(h(s,b,\theta))}<br>\end{equation}<br>其中$h(s,a,\theta)$可以通过神经网络学习得到（这样上式其实就是一个多分类器的最后一个softmax FC层），也可以是特征的线性回归$h(s,a,\theta)=\theta^{\mathsf{T}}x(s,a)$。<br>对于连续的action空间，我们可以用一个连续的概率密度函数来表达$\pi(a|s,\theta)$，比如正态分布。<br>
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