Distributed Online Submodular Maximization under Communication Delays: A Simultaneous Decision-Making Approach

TL;DR

This paper introduces a distributed online algorithm, DOG, for multi-agent submodular maximization that effectively manages communication delays and arbitrary network topologies, balancing coordination quality and convergence speed.

Contribution

The paper presents the DOG algorithm, integrating adversarial bandit learning with delayed feedback, enabling simultaneous multi-agent decision-making in dynamic, delayed communication environments.

Findings

DOG achieves approximation guarantees relative to an optimal solution.

The algorithm balances coordination performance and convergence time based on communication delays.

DOG generalizes between centralized and decentralized online coordination approaches.

Abstract

We provide a distributed online algorithm for multi-agent submodular maximization under communication delays. We are motivated by the future distributed information-gathering tasks in unknown and dynamic environments, where utility functions naturally exhibit the diminishing-returns property, i.e., submodularity. Existing approaches for online submodular maximization either rely on sequential multi-hop communication, resulting in prohibitive delays and restrictive connectivity assumptions, or restrict each agent's coordination to its one-hop neighborhood only, thereby limiting the coordination performance. To address the issue, we provide the Distributed Online Greedy (DOG) algorithm, which integrates tools from adversarial bandit learning with delayed feedback to enable simultaneous decision-making across arbitrary network topologies. We provide the approximation performance of DOG against an optimal solution, capturing the suboptimality cost due to decentralization as a function of the network structure. Our analyses further reveal a trade-off between coordination performance and convergence time, determined by the magnitude of communication delays. By this trade-off, DOG spans the spectrum between the state-of-the-art fully centralized online coordination approach [1] and fully decentralized one-hop coordination approach [2].