Researchers present a unified mathematical framework for certifying locality in scalable multi-agent reinforcement learning (MARL) systems by decomposing the state-transition matrix into environment and policy sensitivity components. The approach uses spectral radius analysis to weaken prior Dobrushin bounds and applies temperature-scaled softmax policies to control locality, enabling exponentially decaying truncation bias in networked agent systems.
This theoretical computer science contribution addresses a fundamental challenge in distributed multi-agent reinforcement learning: determining when local agent neighborhoods provide sufficient information for effective planning without requiring global system knowledge. The standard approach using Dobrushin row-sum bounds often proves overly conservative because it assumes worst-case action selections that realistic policies never take.
The innovation lies in decomposing the combined state-transition matrix C^π into two independent components—environment dynamics (E^s) and action sensitivity (E^a)—coupled with policy reactivity (Π(π)). This separation enables tighter spectral bounds than previous supremum-based approaches. For practical softmax policies, the temperature parameter τ directly controls the degree of locality, providing a concrete hyperparameter for practitioners. The connection between softmax temperature and value decay represents an elegant bridge between optimization design choices and distributed system properties.
The framework's impact extends to algorithm design through the block-coordinate KL-proximal policy-improvement guarantee, which proves truncation bias decays exponentially with message-passing radius κ. This ensures that limiting agent communication to local neighborhoods incurs controlled approximation error, validating scalable MARL architectures used in swarm robotics, traffic control, and game-playing systems.
For researchers developing distributed reinforcement learning systems, this work provides tighter theoretical justification for locality assumptions and principled guidance on softmax temperature selection. The spectral radius framework applies to broader settings where prior Dobrushin-style analysis fails, potentially enabling MARL applications in higher-dimensional or more densely connected agent networks.
- →Decomposing state-transition matrices into environment and policy components yields tighter locality bounds than previous supremum-based Dobrushin approaches
- →Softmax temperature directly controls value-function locality decay in networked multi-agent systems
- →Spectral radius certification (ρ(H^π)<1) is strictly weaker than row-sum conditions for the same matrix
- →Truncation bias from limiting agent communication decays exponentially with message-passing radius under the proposed framework
- →The theoretical results apply to deterministic policy-improvement algorithms with formal convergence guarantees