Hardness in Markov Decision Processes: Theory and Practice

Meticulously analysing the empirical strengths and weaknesses of reinforcement learning methods in hard (challenging) environments is essential to inspire innovations and assess progress in the field. In tabular reinforcement learning, there is no well-established standard selection of environments to conduct such analysis, which is partially due to the lack of a widespread understanding of the rich theory of hardness of environments. The goal of this paper is to unlock the practical usefulness of this theory through four main contributions. First, we present a systematic survey of the theory of hardness, which also identifies promising research directions. Second, we introduce \texttt{Colosseum}, a pioneering package that enables empirical hardness analysis and implements a principled benchmark composed of environments that are diverse with respect to different measures of hardness.