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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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<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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