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

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