Near-Optimal Multi-Agent Learning for Safe Coverage Control

In multi-agent coverage control problems, agents navigate their environment to reach locations that maximize the coverage of some density. In practice, the density is rarely known textita priori, further complicating the original NP-hard problem. Moreover, in many applications, agents cannot visit arbitrary locations due to textita priori unknown safety constraints. In this paper, we aim to efficiently learn the density to approximately solve the coverage problem while preserving the agents' safety. We first propose a conditionally linear submodular coverage function that facilitates theoretical analysis. Utilizing this structure, we develop MacOpt, a novel algorithm that efficiently trades off the exploration-exploitation dilemma due to partial observability, and show that it achieves sublinear regret. Next, we extend results on single-agent safe exploration to our multi-agent setting and propose SafeMac for safe coverage and exploration. We analyze SafeMac and give first of its kind results: near optimal coverage in finite time while provably guaranteeing safety. We extensively evaluate our algorithms on synthetic and real problems, including a bio-diversity monitoring task under safety constraints, where SafeMac outperforms competing methods.