Model-Free Robust ϕ-Divergence Reinforcement Learning Using Both Offline and Online Data

The goal of robust reinforcement learning (RL) is to learn a policy that is robust against the uncertainty in model parameters. Parameter uncertainty commonly occurs in many real-world RL applications due to simulator modeling errors, changes in the real-world system dynamics over time, and adversarial disturbances. Robust RL is typically formulated as a max-min problem, where the objective is to learn the policy that maximizes the value against the worst possible models that lie in an uncertainty set. In this work, we propose a robust RL algorithm called Robust Fitted Q-Iteration (RFQI), which uses only an offline dataset to learn the optimal robust policy. Robust RL with offline data is significantly more challenging than its non-robust counterpart because of the minimization over all models present in the robust Bellman operator. This poses challenges in offline data collection, optimization over the models, and unbiased estimation. In this work, we propose a systematic approach to overcome these challenges, resulting in our RFQI algorithm. We prove that RFQI learns a near-optimal robust policy under standard assumptions and demonstrate its superior performance on standard benchmark problems. In this work, we study the problem of developing a robust RL algorithm with provably optimal performance for an RMDP with arbitrarily large state spaces, using only offline data with function approximation. Before stating the contributions of our work, we provide a brief overview of the results in offline and robust RL that are directly related to ours. We leave a more thorough discussion on related works to Appendix D. Offline RL: Offline RL considers the problem of learning the optimal policy only using a pre-collected (offline) dataset. Offline RL problem has been addressed extensively in the literature (