On the Stability and Convergence of Robust Adversarial Reinforcement Learning: A Case Study on Linear Quadratic Systems

Reinforcement learning (RL) algorithms can fail to generalize due to the gap between the simulation and the real world. One standard remedy is to use robust adversarial RL (RARL) that accounts for this gap during the policy training, by modeling the gap as an adversary against the training agent. In this work, we reexamine the effectiveness of RARL under a fundamental robust control setting: the linear quadratic (LQ) case. We first observe that the popular RARL scheme that greedily alternates agents’ updates can easily destabilize the system. Motivated by this, we propose several other policy-based RARL algorithms whose convergence behaviors are then studied both empirically and theoretically. We find: i) the conventional RARL framework (Pinto et al., 2017) can learn a destabilizing policy if the initial policy does not enjoy the robust stability property against the adversary; and ii) with robustly stabilizing initializations, our proposed double-loop RARL algorithm provably converges to the global optimal cost while maintaining robust stability on-the-fly. We also examine the stability and convergence issues of other variants of policy-based RARL algorithms, and then discuss several ways to learn robustly stabilizing initializations. From a robust control perspective, we aim to provide some new and critical angles about RARL, by identifying and addressing the stability issues in this fundamental LQ setting in continuous control. Our results make an initial attempt toward better theoretical understandings of policy-based RARL, the core approach in Pinto et al., 2017.