Optimality Gap of Decentralized Submodular Maximization under Probabilistic Communication

TL;DR

This paper analyzes the impact of probabilistic communication on the optimality gap in decentralized submodular maximization, providing theoretical insights and practical implications for systems with unreliable communication.

Contribution

It introduces a probabilistic optimality gap framework considering communication success rates, guiding message-passing strategies in resource-limited decentralized systems.

Findings

Probabilistic communication affects the optimality gap significantly.

Strategic message-passing improves solution quality under communication uncertainty.

Numerical example validates the theoretical analysis.

Abstract

This paper considers the problem of decentralized submodular maximization subject to partition matroid constraint using a sequential greedy algorithm with probabilistic inter-agent message-passing. We propose a communication-aware framework where the probability of successful communication between connected devices is considered. Our analysis introduces the notion of the probabilistic optimality gap, highlighting its potential influence on determining the message-passing sequence based on the agent's broadcast reliability and strategic decisions regarding agents that can broadcast their messages multiple times in a resource-limited environment. This work not only contributes theoretical insights but also has practical implications for designing and analyzing decentralized systems in uncertain communication environments. A numerical example demonstrates the impact of our results.