  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 $\textit{a priori}$, further complicating the original
NP-hard problem. Moreover, in many applications, agents cannot visit arbitrary
locations due to $\textit{a priori}$ 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.
