Policy Synthesis for Factored MDPs with Graph Temporal Logic Specifications

TL;DR

This paper presents a distributed algorithm for synthesizing policies in multi-agent systems with spatial-temporal tasks, leveraging factored MDPs and graph temporal logic to enable scalable solutions.

Contribution

It introduces a novel distributed synthesis method that decomposes complex multi-agent policy problems into smaller, agent-specific problems with linear runtime in the number of agents.

Findings

Algorithm scales to hundreds of agents

Runs in linear time relative to total agents

Exponential complexity only in local neighborhood size

Abstract

We study the synthesis of policies for multi-agent systems to implement spatial-temporal tasks. We formalize the problem as a factored Markov decision process subject to so-called graph temporal logic specifications. The transition function and the spatial-temporal task of each agent depend on the agent itself and its neighboring agents. The structure in the model and the specifications enable to develop a distributed algorithm that, given a factored Markov decision process and a graph temporal logic formula, decomposes the synthesis problem into a set of smaller synthesis problems, one for each agent. We prove that the algorithm runs in time linear in the total number of agents. The size of the synthesis problem for each agent is exponential only in the number of neighboring agents, which is typically much smaller than the number of agents. We demonstrate the algorithm in case studies on disease control and urban security. The numerical examples show that the algorithm can scale to hundreds of agents.