Learning NP-Hard Multi-Agent Assignment Planning using GNN: Inference on a Random Graph and Provable Auction-Fitted Q-learning

TL;DR

This paper introduces a novel learning-based approach using GNNs and probabilistic graphical models to efficiently solve complex multi-agent scheduling problems with near-optimal solutions and transferability across problem instances.

Contribution

It develops a mean-field inference method for random PGMs and proposes an order-transferable Q-function estimator with auction-based joint assignment, enabling polynomial-time solutions with provable near-optimality.

Findings

Achieves at least 1-1/e optimality in MRRC problems.

Demonstrates near-optimal and transferable solutions in experiments.

Extends methods to IPMS and minimax-mTSP problems.

Abstract

This paper explores the possibility of near-optimally solving multi-agent, multi-task NP-hard planning problems with time-dependent rewards using a learning-based algorithm. In particular, we consider a class of robot/machine scheduling problems called the multi-robot reward collection problem (MRRC). Such MRRC problems well model ride-sharing, pickup-and-delivery, and a variety of related problems. In representing the MRRC problem as a sequential decision-making problem, we observe that each state can be represented as an extension of probabilistic graphical models (PGMs), which we refer to as random PGMs. We then develop a mean-field inference method for random PGMs. We then propose (1) an order-transferable Q-function estimator and (2) an order-transferability-enabled auction to select a joint assignment in polynomial time. These result in a reinforcement learning framework with at least $1-1/e$ optimality. Experimental results on solving MRRC problems highlight the near-optimality and transferability of the proposed methods. We also consider identical parallel machine scheduling problems (IPMS) and minimax multiple traveling salesman problems (minimax-mTSP).