Is a Good Representation Sufficient for Sample Efficient Reinforcement Learning?

TL;DR

This paper investigates the limitations of good representations in achieving sample-efficient reinforcement learning, revealing that representation quality alone is insufficient unless it surpasses certain thresholds, with implications for various learning paradigms.

Contribution

The work establishes sharp thresholds for representation quality necessary for sample-efficient RL and demonstrates fundamental limitations and exponential separations between different learning methods.

Findings

Good representations are not sufficient for sample-efficient RL without passing certain quality thresholds.

There are fundamental lower bounds on the dimensionality of representations for effective RL.

Exponential sample complexity gaps exist between perfect and suboptimal representations across learning paradigms.

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.