Exploiting Anonymity in Approximate Linear Programming: Scaling to Large Multiagent MDPs (Extended Version)

TL;DR

This paper introduces an approach leveraging anonymity in multiagent factored MDPs to improve the scalability of approximate linear programming, enabling solutions for larger, more complex problems.

Contribution

It presents a novel method exploiting anonymous influence to reduce complexity and scale approximate linear programming to previously unsolvable large multiagent MDPs.

Findings

Successfully scaled LP solutions to a 50-node disease control problem with 25 agents.

Demonstrated computational efficiency gains from exploiting anonymity.

Achieved solution for dense multiagent systems previously infeasible.

Abstract

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.