Toward Finding Strong Pareto Optimal Policies in Multi-Agent Reinforcement Learning
This addresses a key limitation in cooperative multi-agent systems by ensuring robust optimal policies, though it is incremental as it builds on existing gradient descent methods.
The paper tackles the problem of achieving Pareto optimal policies in multi-agent reinforcement learning by showing that standard methods converge to weak Pareto solutions, and proposes MGDA++ to ensure strong Pareto optimality, with theoretical convergence proven for convex bi-objective problems and demonstrated efficiency in Gridworld benchmarks.
In this work, we study the problem of finding Pareto optimal policies in multi-agent reinforcement learning problems with cooperative reward structures. We show that any algorithm where each agent only optimizes their reward is subject to suboptimal convergence. Therefore, to achieve Pareto optimality, agents have to act altruistically by considering the rewards of others. This observation bridges the multi-objective optimization framework and multi-agent reinforcement learning together. We first propose a framework for applying the Multiple Gradient Descent algorithm (MGDA) for learning in multi-agent settings. We further show that standard MGDA is subjected to weak Pareto convergence, a problem that is often overlooked in other learning settings but is prevalent in multi-agent reinforcement learning. To mitigate this issue, we propose MGDA++, an improvement of the existing algorithm to handle the weakly optimal convergence of MGDA properly. Theoretically, we prove that MGDA++ converges to strong Pareto optimal solutions in convex, smooth bi-objective problems. We further demonstrate the superiority of our MGDA++ in cooperative settings in the Gridworld benchmark. The results highlight that our proposed method can converge efficiently and outperform the other methods in terms of the optimality of the convergent policies. The source code is available at \url{https://github.com/giangbang/Strong-Pareto-MARL}.