  Traditional approaches to the design of multi-agent navigation algorithms
consider the environment as a fixed constraint, despite the obvious influence
of spatial constraints on agents' performance. Yet hand-designing improved
environment layouts and structures is inefficient and potentially expensive.
The goal of this paper is to consider the environment as a decision variable in
a system-level optimization problem, where both agent performance and
environment cost can be accounted for. We begin by proposing a novel
environment optimization problem. We show, through formal proofs, under which
conditions the environment can change while guaranteeing completeness (i.e.,
all agents reach their navigation goals). Our solution leverages a model-free
reinforcement learning approach. In order to accommodate a broad range of
implementation scenarios, we include both online and offline optimization, and
both discrete and continuous environment representations. Numerical results
corroborate our theoretical findings and validate our approach.
