Pathwise Information Certificates for Decentralized Adaptive Sensing
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.
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BibTeX
@misc{tsiligkaridis2026pathwise,
title = {{Pathwise Information Certificates for Decentralized Adaptive Sensing}},
author = {Theodoros Tsiligkaridis},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10362},
eprint = {2610.10362},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10362},
}
RIS
TY - UNPB
TI - Pathwise Information Certificates for Decentralized Adaptive Sensing
AU - Theodoros Tsiligkaridis
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10362
UR - https://arxiv.org/abs/2610.10362
AB - 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.
ER -