Lyapunov Robust Constrained-MDPs: Soft-Constrained Robustly Stable Policy Optimization under Model Uncertainty

Safety and robustness are two desired properties for any reinforcement learning algorithm. CMDPs can handle additional safety constraints and RMDPs can perform well under model uncertainties. In this paper, we propose to unite these two frameworks resulting in robust constrained MDPs (RCMDPs). The motivation is to develop a framework that can satisfy safety constraints while also simultaneously offer robustness to model uncertainties. We develop the RCMDP objective, derive gradient update formula to optimize this objective and then propose policy gradient based algorithms. We also independently propose Lyapunov based reward shaping for RCMDPs, yielding better stability and convergence properties.