  Constrained Markov games offer a formal mathematical framework for modeling
multi-agent reinforcement learning problems where the behavior of the agents is
subject to constraints. In this work, we focus on the recently introduced class
of constrained Markov Potential Games. While centralized algorithms have been
proposed for solving such constrained games, the design of converging
independent learning algorithms tailored for the constrained setting remains an
open question. We propose an independent policy gradient algorithm for learning
approximate constrained Nash equilibria: Each agent observes their own actions
and rewards, along with a shared state. Inspired by the optimization
literature, our algorithm performs proximal-point-like updates augmented with a
regularized constraint set. Each proximal step is solved inexactly using a
stochastic switching gradient algorithm. Notably, our algorithm can be
implemented independently without a centralized coordination mechanism
requiring turn-based agent updates. Under some technical constraint
qualification conditions, we establish convergence guarantees towards
constrained approximate Nash equilibria. We perform simulations to illustrate
our results.
