  The sim-to-real gap, which represents the disparity between training and
testing environments, poses a significant challenge in reinforcement learning
(RL). A promising approach to addressing this challenge is distributionally
robust RL, often framed as a robust Markov decision process (RMDP). In this
framework, the objective is to find a robust policy that achieves good
performance under the worst-case scenario among all environments within a
pre-specified uncertainty set centered around the training environment. Unlike
previous work, which relies on a generative model or a pre-collected offline
dataset enjoying good coverage of the deployment environment, we tackle robust
RL via interactive data collection, where the learner interacts with the
training environment only and refines the policy through trial and error. In
this robust RL paradigm, two main challenges emerge: managing distributional
robustness while striking a balance between exploration and exploitation during
data collection. Initially, we establish that sample-efficient learning without
additional assumptions is unattainable owing to the curse of support shift;
i.e., the potential disjointedness of the distributional supports between the
training and testing environments. To circumvent such a hardness result, we
introduce the vanishing minimal value assumption to RMDPs with a
total-variation (TV) distance robust set, postulating that the minimal value of
the optimal robust value function is zero. We prove that such an assumption
effectively eliminates the support shift issue for RMDPs with a TV distance
robust set, and present an algorithm with a provable sample complexity
guarantee. Our work makes the initial step to uncovering the inherent
difficulty of robust RL via interactive data collection and sufficient
conditions for designing a sample-efficient algorithm accompanied by sharp
sample complexity analysis.
