Ruicheng Ao

Ruicheng Ao, Shicong Cen, Yuejie Chi

Finding equilibria via gradient play in competitive multi-agent games has been attracting a growing amount of attention in recent years, with emphasis on designing efficient strategies where the agents operate in a decentralized and symmetric manner with guaranteed convergence. While significant efforts have been made in understanding zero-sum two-player matrix games, the performance in zero-sum multi-agent games remains inadequately explored, especially in the presence of delayed feedbacks, leaving the scalability and resiliency of gradient play open to questions. In this paper, we make progress by studying asynchronous gradient plays in zero-sum polymatrix games under delayed feedbacks. We first establish that the last iterate of entropy-regularized optimistic multiplicative weight updates (OMWU) method converges linearly to the quantal response equilibrium (QRE), the solution concept under bounded rationality, in the absence of delays. While the linear convergence continues to hold even when the feedbacks are randomly delayed under mild statistical assumptions, it converges at a noticeably slower rate due to a smaller tolerable range of learning rates. Moving beyond, we demonstrate entropy-regularized OMWU -- by adopting two-timescale learning rates in a delay-aware manner -- enjoys faster last-iterate convergence under fixed delays, and continues to converge provably even when the delays are arbitrarily bounded in an average-iterate manner. Our methods also lead to finite-time guarantees to approximate the Nash equilibrium (NE) by moderating the amount of regularization. To the best of our knowledge, this work is the first that aims to understand asynchronous gradient play in zero-sum polymatrix games under a wide range of delay assumptions, highlighting the role of learning rates separation.

Ruicheng Ao, Siyang Gao, David Simchi-Levi

This technical note studies the reliability limits of LLM-based multi-agent planning as a delegated decision problem. We model the LLM-based multi-agent architecture as a finite acyclic decision network in which multiple stages process shared model-context information, communicate through language interfaces with limited capacity, and may invoke human review. We show that, without new exogenous signals, any delegated network is decision-theoretically dominated by a centralized Bayes decision maker with access to the same information. In the common-evidence regime, this implies that optimizing over multi-agent directed acyclic graphs under a finite communication budget can be recast as choosing a budget-constrained stochastic experiment on the shared signal. We also characterize the loss induced by communication and information compression. Under proper scoring rules, the gap between the centralized Bayes value and the value after communication admits an expected posterior divergence representation, which reduces to conditional mutual information under logarithmic loss and to expected squared posterior error under the Brier score. These results characterize the fundamental reliability limits of delegated LLM planning. Experiments with LLMs on a controlled problem set further demonstrate these characterizations.