The Importance of System-Level Information in Multiagent Systems Design: Cardinality and Covering Problems

TL;DR

This paper investigates how uncertainty in system-level information, specifically cardinality, impacts multiagent resource allocation, and proposes a distributed learning algorithm to improve control performance under such uncertainty.

Contribution

It introduces a fundamental tradeoff analysis for uncertain cardinality in covering problems and presents a distributed algorithm that learns and adapts to this cardinality.

Findings

The tradeoff between information value and risk in control design is characterized.

The proposed algorithm learns the cardinality effectively, matching or surpassing known-optimal performance.

Distributed learning improves control in uncertain information scenarios.

Abstract

A fundamental challenge in multiagent systems is to design local control algorithms to ensure a desirable collective behaviour. The information available to the agents, gathered either through communication or sensing, naturally restricts the achievable performance. Hence, it is fundamental to identify what piece of information is valuable and can be exploited to design control laws with enhanced performance guarantees. This paper studies the case when such information is uncertain or inaccessible for a class of submodular resource allocation problems termed covering problems. In the first part of this work we pinpoint a fundamental risk-reward tradeoff faced by the system operator when conditioning the control design on a valuable but uncertain piece of information, which we refer to as the cardinality, that represents the maximum number of agents that can simultaneously select any given resource. Building on this analysis, we propose a distributed algorithm that allows agents to learn the cardinality while adjusting their behaviour over time. This algorithm is proved to perform on par or better to the optimal design obtained when the exact cardinality is known a priori.