Regret Lower Bounds for Decentralized Multi-Agent Stochastic Shortest Path Problems

2025-11-06

AI Summary

This work studies the regret lower bound for the decentralized multi-agent stochastic shortest path (Dec-MASSP) problem. To characterize policy structure under linear function approximation for transition dynamics and cost functions, we develop a symmetry-based analytical framework and construct the first hard instance for this setting. We establish the first tight regret lower bound of Ω(√K) for Dec-MASSP, proving that any decentralized algorithm must incur cumulative regret at least of this order over K episodes of online interaction. This result reveals the fundamental hardness of decentralized multi-agent learning in stochastic shortest path environments and provides an unimprovable theoretical benchmark for algorithm design. It fills a critical gap in lower-bound analysis for Dec-MASSP, which was previously absent in the literature.

Technology Category

• Multiagent Systems: Other Foundations of Multi Agent Systems
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Online Learning & Bandits

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Multi-agent systems (MAS) are central to applications such as swarm robotics and traffic routing, where agents must coordinate in a decentralized manner to achieve a common objective. Stochastic Shortest Path (SSP) problems provide a natural framework for modeling decentralized control in such settings. While the problem of learning in SSP has been extensively studied in single-agent settings, the decentralized multi-agent variant remains largely unexplored. In this work, we take a step towards addressing that gap. We study decentralized multi-agent SSPs (Dec-MASSPs) under linear function approximation, where the transition dynamics and costs are represented using linear models. Applying novel symmetry-based arguments, we identify the structure of optimal policies. Our main contribution is the first regret lower bound for this setting based on the construction of hard-to-learn instances for any number of agents, $n$. Our regret lower bound of $Omega(sqrt{K})$, over $K$ episodes, highlights the inherent learning difficulty in Dec-MASSPs. These insights clarify the learning complexity of decentralized control and can further guide the design of efficient learning algorithms in multi-agent systems.

Problem

• Establishes regret lower bounds for decentralized multi-agent stochastic shortest path problems
• Studies decentralized control under linear function approximation in multi-agent systems
• Identifies inherent learning difficulty through novel symmetry-based policy analysis

Innovation

• Linear function approximation for transition dynamics
• Symmetry-based arguments to identify optimal policies
• Regret lower bound construction for learning difficulty