A Unified Framework for Locality in Scalable MARL

2026-02-18

AI Summary

This work addresses the challenge of scalability in multi-agent reinforcement learning, where global coupling is hindered by the curse of dimensionality and existing approaches impose overly conservative assumptions on locality. The paper proposes a unified framework that, for the first time, models locality as a policy-dependent phenomenon. By decomposing the policy-induced interaction matrix, it reveals a synergistic mechanism through which environmental structure and policy sensitivity jointly shape locality. Leveraging spectral analysis and block coordinate policy optimization, the authors derive a tighter spectral condition—ρ(Eˢ + EᵃΠ(π)) < 1—that strictly improves upon prior norm-based conditions. Building on this, they establish a theoretically grounded localized policy improvement framework that elucidates the fundamental trade-off between locality and optimality.

Technology Category

• Multiagent Systems: Multiagent Learning
• Search and Optimization: Learning to Search
• Machine Learning: Reinforcement Learning

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements

Abstract

Scalable Multi-Agent Reinforcement Learning (MARL) is fundamentally challenged by the curse of dimensionality. A common solution is to exploit locality, which hinges on an Exponential Decay Property (EDP) of the value function. However, existing conditions that guarantee the EDP are often conservative, as they are based on worst-case, environment-only bounds (e.g., supremums over actions) and fail to capture the regularizing effect of the policy itself. In this work, we establish that locality can also be a \emph{policy-dependent} phenomenon. Our central contribution is a novel decomposition of the policy-induced interdependence matrix, $H^π$, which decouples the environment's sensitivity to state ($E^{\mathrm{s}}$) and action ($E^{\mathrm{a}}$) from the policy's sensitivity to state ($Π(π)$). This decomposition reveals that locality can be induced by a smooth policy (small $Π(π)$) even when the environment is strongly action-coupled, exposing a fundamental locality-optimality tradeoff. We use this framework to derive a general spectral condition $ρ(E^{\mathrm{s}}+E^{\mathrm{a}}Π(π)) < 1$ for exponential decay, which is strictly tighter than prior norm-based conditions. Finally, we leverage this theory to analyze a provably-sound localized block-coordinate policy improvement framework with guarantees tied directly to this spectral radius.

Problem

• Scalable MARL
• Locality
• Exponential Decay Property
• Policy-dependent
• Curse of Dimensionality

Innovation

• policy-dependent locality
• interdependence matrix decomposition
• exponential decay property
• spectral condition
• localized policy improvement