利用近似线性规划中的相似性：扩展到大型多智能体MDP（扩展版）
Exploiting Anonymity in Approximate Linear Programming: Scaling to Large Multiagent MDPs (Extended Version)
摘要：
马尔可夫决策过程（MDP）的许多精确和近似的解决方法试图利用问题的结构，并基于价值函数的因式分解。然而，特别是多智能体设置，众所周知，遭受指数增长的价值组件的大小，因为相互作用变得更加密集，这意味着近似架构的限制，在问题的大小和类型，他们可以处理。我们提出了一种方法来减轻这种限制，某些类型的多智能体系统，利用一个属性，可以被认为是“匿名影响”的因素MDP。匿名影响有效地总结了联合变量的影响时，显式表示的变量身份的问题可以避免。我们展示了如何从匿名的代表性的好处转化为计算效率，无论是一般的变量消除因子图，但特别是也为近似的线性规划解决方案，因子化的MDP。后者允许将线性规划扩展到以前无法解决的分解的MDP。我们的研究结果显示，在一个密集连接的图与50个节点和25个代理的随机疾病过程的控制。
英文摘要：
Many exact and approximate solution methods for Markov Decision Processes (MDPs) attempt to exploit structure in the problem and are based on factorization of the value function. Especially multiagent settings, however, are known to suffer from an exponential increase in value component sizes as interactions become denser, meaning that approximation architectures are restricted in the problem sizes and types they can handle. We present an approach to mitigate this limitation for certain types of multiagent systems, exploiting a property that can be thought of as "anonymous influence" in the factored MDP. Anonymous influence summarizes joint variable effects efficiently whenever the explicit representation of variable identity in the problem can be avoided. We show how representational benefits from anonymity translate into computational efficiencies, both for general variable elimination in a factor graph but in particular also for the approximate linear programming solution to factored MDPs. The latter allows to scale linear programming to factored MDPs that were previously unsolvable. Our results are shown for the control of a stochastic disease process over a densely connected graph with 50 nodes and 25 agents.
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