IMAS$^2$: Joint Agent Selection and Information-Theoretic Coordinated Perception In Dec-POMDPs

We study the problem of jointly selecting sensing agents and synthesizing decentralized active perception policies for the chosen subset of agents within a Decentralized Partially Observable Markov Decision Process (Dec-POMDP) framework. Our approach employs a two-layer optimization structure. In the inner layer, we introduce information-theoretic metrics, defined by the mutual information between the unknown trajectories or some hidden property in the environment and the collective partial observations in the multi-agent system, as a unified objective for active perception problems. We employ various optimization methods to obtain optimal sensor policies that maximize mutual information for distinct active perception tasks. In the outer layer, we prove that under certain conditions, the information-theoretic objectives are monotone and submodular with respect to the subset of observations collected from multiple agents. We then exploit this property to design an IMAS$^2$ (Information-theoretic Multi-Agent Selection and Sensing) algorithm for joint sensing agent selection and sensing policy synthesis. However, since the policy search space is infinite, we adapt the classical Nemhauser-Wolsey argument to prove that the proposed IMAS$^2$ algorithm can provide a tight $(1 - 1/e)$-guarantee on the performance. Finally, we demonstrate the effectiveness of our approach in a multi-agent cooperative perception in a grid-world environment.