Is a Good Representation Sufficient for Sample Efficient Reinforcement Learning?
Simon S. Du, Sham M. Kakade, Ruosong Wang, Lin F. Yang
TL;DR
The paper challenges the notion that a good representation suffices for sample-efficient reinforcement learning by proving exponential lower bounds for value-based, model-based, and policy-based methods under linear function approximation. These results hold even when the transition model is known and the representation yields near-linear predictions, highlighting that representation quality alone imposes hard thresholds on efficiency. The findings imply substantial separations between RL paradigms and between RL and supervised/imitation learning, underscoring the need for additional structural assumptions beyond representation quality. The work clarifies fundamental statistical limits of RL with function approximation and motivates seeking new conditions to achieve practical sample efficiency.
Abstract
Modern deep learning methods provide effective means to learn good representations. However, is a good representation itself sufficient for sample efficient reinforcement learning? This question has largely been studied only with respect to (worst-case) approximation error, in the more classical approximate dynamic programming literature. With regards to the statistical viewpoint, this question is largely unexplored, and the extant body of literature mainly focuses on conditions which permit sample efficient reinforcement learning with little understanding of what are necessary conditions for efficient reinforcement learning. This work shows that, from the statistical viewpoint, the situation is far subtler than suggested by the more traditional approximation viewpoint, where the requirements on the representation that suffice for sample efficient RL are even more stringent. Our main results provide sharp thresholds for reinforcement learning methods, showing that there are hard limitations on what constitutes good function approximation (in terms of the dimensionality of the representation), where we focus on natural representational conditions relevant to value-based, model-based, and policy-based learning. These lower bounds highlight that having a good (value-based, model-based, or policy-based) representation in and of itself is insufficient for efficient reinforcement learning, unless the quality of this approximation passes certain hard thresholds. Furthermore, our lower bounds also imply exponential separations on the sample complexity between 1) value-based learning with perfect representation and value-based learning with a good-but-not-perfect representation, 2) value-based learning and policy-based learning, 3) policy-based learning and supervised learning and 4) reinforcement learning and imitation learning.