Online Robust Reinforcement Learning with Model Uncertainty
This work addresses the problem of robust policy optimization in uncertain environments for RL practitioners, offering incremental improvements with theoretical guarantees.
The paper tackles robust reinforcement learning under model uncertainty by developing online, sample-based algorithms for both tabular and function approximation settings, proving convergence and finite-time error bounds comparable to non-robust methods.
Robust reinforcement learning (RL) is to find a policy that optimizes the worst-case performance over an uncertainty set of MDPs. In this paper, we focus on model-free robust RL, where the uncertainty set is defined to be centering at a misspecified MDP that generates a single sample trajectory sequentially and is assumed to be unknown. We develop a sample-based approach to estimate the unknown uncertainty set and design a robust Q-learning algorithm (tabular case) and robust TDC algorithm (function approximation setting), which can be implemented in an online and incremental fashion. For the robust Q-learning algorithm, we prove that it converges to the optimal robust Q function, and for the robust TDC algorithm, we prove that it converges asymptotically to some stationary points. Unlike the results in [Roy et al., 2017], our algorithms do not need any additional conditions on the discount factor to guarantee the convergence. We further characterize the finite-time error bounds of the two algorithms and show that both the robust Q-learning and robust TDC algorithms converge as fast as their vanilla counterparts(within a constant factor). Our numerical experiments further demonstrate the robustness of our algorithms. Our approach can be readily extended to robustify many other algorithms, e.g., TD, SARSA, and other GTD algorithms.