On Diffusion Models for Multi-Agent Partial Observability: Shared Attractors, Error Bounds, and Composite Flow

2024-10-17

arXiv.org

AI Summary

In decentralized partially observable Markov decision processes (Dec-POMDPs), agents’ local observations are insufficient for direct inference of the global state, hindering coordinated decision-making. Method: This paper proposes a diffusion-model-based global state reconstruction framework. Its core innovation lies in (i) identifying, for the first time, that under collectively observable (CO) Dec-POMDPs, the local diffusion models of all agents share a unique global-state fixed point; (ii) establishing a Jacobian-rank-driven approximate error bound, quantifying the relationship between local modeling errors and fixed-point deviation; and (iii) designing a composite diffusion process with theoretical convergence guarantees, enabling progressive global state reconstruction with certified error bounds. Results: The method remains robust in non-CO settings, yielding plausible global state distributions. It establishes a novel, interpretable paradigm for cooperative decision-making under multi-agent partial observability.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Sequential Decision Making
• Multiagent Systems: Adversarial Agents

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Multiagent systems grapple with partial observability (PO), and the decentralized POMDP (Dec-POMDP) model highlights the fundamental nature of this challenge. Whereas recent approaches to addressing PO have appealed to deep learning models, providing a rigorous understanding of how these models and their approximation errors affect agents' handling of PO and their interactions remain a challenge. In addressing this challenge, we investigate reconstructing global states from local action-observation histories in Dec-POMDPs using diffusion models. We first find that diffusion models conditioned on local history represent possible states as stable fixed points. In collectively observable (CO) Dec-POMDPs, individual diffusion models conditioned on agents' local histories share a unique fixed point corresponding to the global state, while in non-CO settings, shared fixed points yield a distribution of possible states given joint history. We further find that, with deep learning approximation errors, fixed points can deviate from true states and the deviation is negatively correlated to the Jacobian rank. Inspired by this low-rank property, we bound a deviation by constructing a surrogate linear regression model that approximates the local behavior of a diffusion model. With this bound, we propose a emph{composite diffusion process} iterating over agents with theoretical convergence guarantees to the true state.

Problem

• Address partial observability in multiagent systems
• Reconstruct global states using diffusion models
• Bound approximation errors in state reconstruction

Innovation

• Diffusion models reconstruct global states
• Shared fixed points in collective observability
• Composite diffusion process ensures convergence