Online Robust Reinforcement Learning with General Function Approximation

In many real-world settings, reinforcement learning systems suffer performance degradation when the environment encountered at deployment differs from that observed during training. Distributionally robust reinforcement learning (DR-RL) mitigates this issue by seeking policies that maximize performance under the most adverse transition dynamics within a prescribed uncertainty set. Most existing DR-RL approaches, however, rely on strong data availability assumptions-such as access to a generative model or large offline datasets-and are largely restricted to tabular settings. In this work, we propose a fully online DR-RL algorithm with general function approximation that learns robust policies solely through interaction, without requiring prior knowledge or pre-collected data. Our approach is based on a dual-driven fitted robust Bellman procedure that simultaneously estimates the value function and the corresponding worst-case backup operator. We establish regret guarantees for online DR-RL characterized by an intrinsic complexity notion-the robust Bellman-Eluder dimension covering a broad class of ϕ-divergence uncertainty sets. The resulting regret bounds are sublinear, do not scale with the size of the state or action spaces, and specialize to tight rates in structured problem classes, demonstrating the practicality and scalability of our framework.