  We address the conflicting requirements of a multi-agent assignment problem
through constrained reinforcement learning, emphasizing the inadequacy of
standard regularization techniques for this purpose. Instead, we recur to a
state augmentation approach in which the oscillation of dual variables is
exploited by agents to alternate between tasks. In addition, we coordinate the
actions of the multiple agents acting on their local states through these
multipliers, which are gossiped through a communication network, eliminating
the need to access other agent states. By these means, we propose a distributed
multi-agent assignment protocol with theoretical feasibility guarantees that we
corroborate in a monitoring numerical experiment.
