A Variational Perturbative Approach to Planning in Graph-based Markov Decision Processes

TL;DR

This paper introduces a novel variational perturbation method for planning in graph-based multi-agent Markov decision processes, improving inference accuracy and performance in complex coordination tasks.

Contribution

It presents a new high-order variational approach for approximate inference in large multi-agent networks, outperforming existing methods especially in non-local cost and synchronization tasks.

Findings

Outperforms state-of-the-art methods in non-local cost scenarios

Achieves significant improvements in synchronization tasks

Provides a scalable approximate inference technique for large networks

Abstract

Coordinating multiple interacting agents to achieve a common goal is a difficult task with huge applicability. This problem remains hard to solve, even when limiting interactions to be mediated via a static interaction-graph. We present a novel approximate solution method for multi-agent Markov decision problems on graphs, based on variational perturbation theory. We adopt the strategy of planning via inference, which has been explored in various prior works. We employ a non-trivial extension of a novel high-order variational method that allows for approximate inference in large networks and has been shown to surpass the accuracy of existing variational methods. To compare our method to two state-of-the-art methods for multi-agent planning on graphs, we apply the method different standard GMDP problems. We show that in cases, where the goal is encoded as a non-local cost function, our method performs well, while state-of-the-art methods approach the performance of random guess. In a final experiment, we demonstrate that our method brings significant improvement for synchronization tasks.