Abstract: The robust $\phi$-regularized Markov Decision Process (RRMDP) framework focuses on designing control policies that are robust against parameter uncertainties due to mismatches between the simulator (nominal) model and real-world settings. This work makes *two* important contributions. First, we propose a *model-free* algorithm called *Robust $\phi$-regularized fitted Q-iteration* for learning an $\epsilon$-optimal robust policy that uses only the historical data collected by rolling out a behavior policy (with *robust exploratory* requirement) on the nominal model. To the best of our knowledge, we provide the *first* unified analysis for a class of $\phi$-divergences achieving robust optimal policies in high-dimensional systems of arbitrary large state space with general function approximation. Second, we introduce the *hybrid robust $\phi$-regularized reinforcement learning* framework to learn an optimal robust policy using both historical data and online sampling. Towards this framework, we propose a model-free algorithm called *Hybrid robust Total-variation-regularized Q-iteration*. To the best of our knowledge, we provide the *first* improved out-of-data-distribution assumption in large-scale problems of arbitrary large state space with general function approximation under the hybrid robust $\phi$-regularized reinforcement learning framework.