Policy Optimization and Multi-agent Reinforcement Learning for Mean-variance Team Stochastic Games
This work addresses multi-agent reinforcement learning for risk-aware decision-making in domains like energy management, though it appears incremental as it builds on existing policy optimization methods.
The paper tackles the problem of long-run mean-variance team stochastic games (MV-TSGs), where agents share a common objective but face challenges due to non-additive variance and non-stationarity, by proposing a sensitivity-based optimization approach and algorithms like MV-MAPI and MV-MATRPO, with numerical experiments on energy management in microgrid systems showing convergence to stationary points.
We study a long-run mean-variance team stochastic game (MV-TSG), where each agent shares a common mean-variance objective for the system and takes actions independently to maximize it. MV-TSG has two main challenges. First, the variance metric is neither additive nor Markovian in a dynamic setting. Second, simultaneous policy updates of all agents lead to a non-stationary environment for each individual agent. Both challenges make dynamic programming inapplicable. In this paper, we study MV-TSGs from the perspective of sensitivity-based optimization. The performance difference and performance derivative formulas for joint policies are derived, which provide optimization information for MV-TSGs. We prove the existence of a deterministic Nash policy for this problem. Subsequently, we propose a Mean-Variance Multi-Agent Policy Iteration (MV-MAPI) algorithm with a sequential update scheme, where individual agent policies are updated one by one in a given order. We prove that the MV-MAPI algorithm converges to a first-order stationary point of the objective function. By analyzing the local geometry of stationary points, we derive specific conditions for stationary points to be (local) Nash equilibria, and further, strict local optima. To solve large-scale MV-TSGs in scenarios with unknown environmental parameters, we extend the idea of trust region methods to MV-MAPI and develop a multi-agent reinforcement learning algorithm named Mean-Variance Multi-Agent Trust Region Policy Optimization (MV-MATRPO). We derive a performance lower bound for each update of joint policies. Finally, numerical experiments on energy management in multiple microgrid systems are conducted.