  This paper studies the multi-agent coverage control (MAC) problem where
agents must dynamically learn an unknown density function while performing
coverage tasks. Unlike many current theoretical frameworks that concentrate
solely on the regret occurring at specific targeted sensory locations, our
approach additionally considers the regret caused by transient behavior - the
path from one location and another. We propose the multi-agent coverage control
with the doubling trick (MAC-DT) algorithm and demonstrate that it achieves
(approximated) regret of $\widetilde{O}(\sqrt{T})$ even when accounting for the
transient behavior. Our result is also supported by numerical experiments,
showcasing that the proposed algorithm manages to match or even outperform the
baseline algorithms in simulation environments. We also show how our algorithm
can be modified to handle safety constraints and further implement the
algorithm on a real-robotic testbed.
