Pathwise Information Certificates for Decentralized Adaptive Sensing

2026-10-07

AI Summary

This study addresses the challenge of quantifying measurement sufficiency in decentralized adaptive sensing by proposing path-based Rényi–Chernoff information certificates. Methodologically, it decouples statistical information from network mixing transients and leverages inverse theorems for pairwise KL divergence alongside topological analysis of multi-agent communication graphs to derive non-asymptotic MAP error bounds and network-wide instantaneous stopping rules for arbitrary history-dependent policies. The core contributions demonstrate that linear growth in accumulated information yields exponential decay in error probability, and identify the weakest competitor as the fundamental bottleneck. Notably, the score of this weakest agent exhibits a significantly stronger correlation with localization speed than average-agent metrics, thereby enabling practical certification and diagnosis of evidence accumulation in decentralized networks.

Abstract

We study decentralized adaptive sensing, where multiple agents choose measurements from evolving local beliefs while exchanging information over a communication graph. We ask whether the measurements actually selected by an adaptive policy have collected enough evidence to distinguish the true target from every plausible alternative. We develop a pathwise certificate based on the Rényi--Chernoff information accumulated along the realized sensing trajectory. It yields nonasymptotic MAP-error bounds and an anytime, network-wide stopping rule for arbitrary history-dependent sensing policies, while separating accumulated statistical information from a bounded network-mixing transient. Linear growth of the information against the least-resolved competitor implies exponential decay of MAP and squared-localization error. A classical pairwise KL converse, specialized to the adaptive decentralized transcript, shows that insufficient information on any pair prevents a positive uniform error exponent, confirming the hardest competitor as a fundamental bottleneck. Across policies, graph topologies, sensor profiles, and seeds, the worst-competitor score correlates more strongly with localization speed than an average-pair proxy in both 1D ($r=0.89$ versus $0.40$) and structured 2D sensing ($r=0.77$ versus $0.48$). Our results provide a practical way to certify and diagnose adaptive multi-agent sensing systems using the evidence they actually collect.

Problem

• decentralized adaptive sensing
• information certificates
• multi-agent systems
• MAP error bounds
• stopping rule

Innovation

• Decentralized adaptive sensing
• Pathwise information certificate
• Rényi-Chernoff information
• Nonasymptotic error bounds
• Worst-competitor bottleneck