Pathwise Information Certificates for Decentralized Adaptive Sensing

A "path-based sensor" produces a single observation along a continuous path. For example, a boolean path-based sensor returns a single "1" if an event of interest is detected at any point along the path and a "0" otherwise. Notably, a "1" provides no direct information about where along the path the event(s) may have occurred. Previous work has demonstrated that observations from multiple path-based sensors can be fused to create a Bayesian belief map over the spatial locations of the underlying event or phenomenon. Moreover, path planning can employ Shannon information theory to accelerate the rate of convergence of the belief map. In this paper, we present a new method to update the belief map based on a path-based sensor observation, and then plan paths to increase information gain. In contrast to prior work that approximates the posterior by averaging over the alternative event histories, we introduce a Bayesian Network (BN) formulation that models the probabilistic relationships between the latent variables and path-based sensor measurements, enabling a more principled Bayesian belief update. We consider static hazard detection in a communication-denied environment as a representative problem setting. The event of a robot returning from its path corresponds to a path-based hazard sensor reading of "0" (hazard not detected), while a robot failing to return corresponds to a reading of "1" (hazard detected). We consider false positives and false negatives. We find that the new method leads to quicker convergence of the belief map than prior work in both single- and multi-robot cases.

In decentralized decision-making, several agents connected according to a network graph aim at solving a classification problem by collecting streaming observations. Due to decentralization, they run an iterative algorithm where, at each iteration, they can only exchange information locally with their neighbors. While decentralized estimation solutions have been shown to match the performance of optimal centralized systems, we show here that surprisingly this conclusion does not hold for decentralized decision-making. Specifically, we prove that the error probability for the best decentralized decision strategy exhibits an irreducible loss with respect to the optimal centralized classifier. This result establishes a fundamental limit for the performance of any decentralized decision strategy. We obtain an analytical relation showing that this limit is related to the interplay between decentralization and classification. The first aspect appears through the distances between the nodes in the graph, while the second aspect plays through the moment generating functions of the likelihood ratios that describe the decision problem. By applying the derived closed-form relation to different network topologies and inference problems, we observe some interesting and perhaps unexpected behavior emerging. In particular, we characterize the scaling law (with the network size) for the loss over popular network topologies, showing that the error probabilities might differ by orders of magnitude; and we examine how performance is affected by the relative distance between informative and uninformative agents over the graph.

We study decentralized multi-agent target search where homogeneous agents communicate intermittently at Poisson-distributed times. Standard unconditional belief fusion wastes communication opportunities by synchronizing agents during high-entropy exploration, when diverse independent beliefs provide better coverage than a premature consensus. We introduce \emph{entropy-gated belief coordination}, in which agents skip fusion while their collective entropy ratio exceeds a threshold~$θ$ and merge only during exploitation, consistent with the bifurcation structure of nonlinear opinion dynamics and the submodular structure of the per-step information gain objective. We further derive $\Istep(α,β)$, the expected mutual information per observation step between two agents' binary sensors, as an interpretable, communication-free measure of sensor informativeness that motivates the gating design and guides system-level analysis. Experiments across 103{,}680 trials (nine grid sizes up to $100{\times}100$, Poisson communication timing, four target movement patterns) show that the Entropy-Gated Trust-Decay Planner (\textsc{EG-TDP}), which adds a detection-probability planner switch in exploitation mode, achieves mean belief quality $\bar{Q}=0.300$ (mean belief mass at the true target cell, averaged across all trials and steps), a $58.9\%$ gain over arithmetic mean and a $37.4\%$ gain over visit-weighted fusion. On representative configurations, EG-TDP also outperforms a joint-Bayesian reference that uses all agents'~observations at every step, despite operating under random intermittent contact only.