Interpreting Primal-Dual Algorithms for Constrained MARL

Constrained multiagent reinforcement learning (C-MARL) is gaining importance as MARL algorithms find new applications in real-world systems ranging from energy systems to drone swarms. Most C-MARL algorithms use a primal-dual approach to enforce constraints through a penalty function added to the reward. In this paper, we study the structural effects of the primal-dual approach on the constraints and value function. First, we show that using the constraint evaluation as the penalty leads to a weak notion of safety, but by making simple modifications to the penalty function, we can enforce meaningful probabilistic safety constraints. Second, we exploit the structural effects of primal-dual methods on value functions, leading to improved value estimates. Simulations in a simple constrained multiagent environment show that our reinterpretation of the primal-dual method in terms of probabilistic constraints is meaningful, and that our proposed value estimation procedure improves convergence to a safe joint policy.