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

Chongyang Shi, Wesley A. Suttle, Michael Dorothy, Jie Fu

TL;DR

This work tackles joint sensing-agent selection and decentralized perception policy design in Dec-POMDPs by formulating a two-layer optimization: an inner information-theoretic objective based on mutual information $I(\cdot;\cdot)$ to drive active perception, and an outer submodular-guided selection of agents and policies. It proves monotone submodularity of information objectives under conditional independence assumptions and introduces IMAS$^2$, a greedy algorithm that achieves a tight $(1-1/e)$-approximation in the presence of infinite policy spaces. The authors develop practical policy-synthesis strategies for both trajectory and secret inference, including a single-agent POMDP-based method and policy-gradient approaches, and validate the framework on a grid-world cooperative-perception task showing efficient convergence and high inference accuracy. The results offer a scalable, theoretically grounded path to joint sensor selection and decentralized perception in uncertain, multi-agent environments with direct applicability to robotics and autonomous sensing systems.

Abstract

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.

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

TL;DR

This work tackles joint sensing-agent selection and decentralized perception policy design in Dec-POMDPs by formulating a two-layer optimization: an inner information-theoretic objective based on mutual information to drive active perception, and an outer submodular-guided selection of agents and policies. It proves monotone submodularity of information objectives under conditional independence assumptions and introduces IMAS, a greedy algorithm that achieves a tight -approximation in the presence of infinite policy spaces. The authors develop practical policy-synthesis strategies for both trajectory and secret inference, including a single-agent POMDP-based method and policy-gradient approaches, and validate the framework on a grid-world cooperative-perception task showing efficient convergence and high inference accuracy. The results offer a scalable, theoretically grounded path to joint sensor selection and decentralized perception in uncertain, multi-agent environments with direct applicability to robotics and autonomous sensing systems.

Abstract

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 (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 algorithm can provide a tight -guarantee on the performance. Finally, we demonstrate the effectiveness of our approach in a multi-agent cooperative perception in a grid-world environment.
Paper Structure (17 sections, 9 theorems, 33 equations, 3 figures, 1 table, 1 algorithm)

This paper contains 17 sections, 9 theorems, 33 equations, 3 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Leveraging Submodularity for Multi-Agent Active Perception
  4. Inferring Latent State Sequence
  5. Inferring Environment State Sequence
  6. Environment Secret Estimation
  7. Approximation Algorithms for Joint Agent Selection and Policy Synthesis
  8. Approximation Algorithm and Performance Guarantee
  9. Policy Synthesis for Maximizing Information Gain
  10. Late state sequence estimation:
  11. Inferring environment state trajectory or secret
  12. Experiment
  13. Partial observable multi-agent system
  14. Inference objective
  15. Observation-based policy space
  16. ...and 2 more sections

Key Result

Lemma 1

Given any $Y_{i } =O_{i,0:T}, Y_{j } = O_{j, 0:T}$ representing agents $i$ and $j$'s observation sequences for a finite horizon $T$ and $X = S_{0:T}$ be the latent state sequence. Under Assumption assumption:independent-obs, $Y_{i }$ and $Y_{j }$ are conditional independent given $X$.

Figures (3)

  • Figure 1: The $10 \times 10$ grid world environment.
  • Figure 2: The sensor range of different actions (Top: small range sensors; Bottom: large range sensors).
  • Figure 3: Comparison of convergence, entropy, and inference performance under different sensing conditions.

Theorems & Definitions (10)

  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Remark 1
  • Lemma 4
  • Corollary 1
  • Lemma 5
  • Lemma 6
  • Proposition 1
  • Theorem 1