Multiagent Reinforcement Learning for Constrained Markov Decision Processes by Consensus-Based Primal–Dual Method

In this work, we consider multiagent reinforcement learning for constrained Markov decision processes and develop a consensus-based primal–dual method to solve the problem, which is model-free and with provable convergence. Compared with existing methods, our algorithm does not require the dynamic model of the system, nor ask the agents to share their local policies. The constraint is incorporated in the objective function to form the Lagrangian with the dual variables updated through the primal–dual method. The consensus-based method is applied to update the parameters of the approximate action-value functions and the dual variables in a distributed manner. The developed algorithm is shown to achieve consensus among the agents and converge to a locally optimal policy. For a certain type of constrained Markov decision processes, the method to ensure the feasibility of the final solution is developed. Numerical results show that the developed algorithm outperforms the multiagent actor–critic algorithm (Liu et al., 2018), which incorporates the constraint in the objective directly.