Is a Good Representation Sufficient for Sample Efficient Reinforcement Learning? (1910.03016v4)

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.

• The paper establishes that representing functions must exceed critical dimensional thresholds to achieve sample-efficient reinforcement learning.
• The paper reveals exponential sample complexity gaps between perfect and imperfect representations, especially in value-based versus policy-based methods.
• The paper demonstrates that even in deterministic systems, ideal feature representations may fail to guarantee sample efficiency, urging deeper algorithmic innovation.

Is a Good Representation Sufficient for Sample Efficient Reinforcement Learning?

In the exploration of reinforcement learning (RL), a pivotal question arises: to what extent is a robust representation sufficient for sample-efficient RL? This paper rigorously examines this in the context of function approximation — particularly, the conditions under which a representation enables efficient RL. It contends that the statistical requirements for sample efficiency in RL with function approximation are more stringent than those implied by the approximation error viewpoint frequently studied in classical dynamic programming.

Main Contributions and Results

The authors delineate their significant findings through several key theoretical contributions:

1. Thresholds for Function Approximation: The research articulates sharp thresholds that identify the limitations of function approximation. Specifically, it underscores that for RL to be sample efficient, the dimensionality of representation must surpass certain thresholds.
2. Exponential Sample Complexity Gaps: The paper reveals exponential separations in sample complexity in several contexts:
   • Between Perfect and Imperfect Representations: Even minor deviations from a perfect linear representation can escalate sample complexity dramatically for value-based methods.
   • Value-Based vs. Policy-Based Learning: The research identifies stark differences, showing that value-based learning can potentially exploit representations more effectively than policy-based methods.
   • Reinforcement Learning vs. Supervised Learning and Imitation Learning: It demonstrates exponential sample complexity increases when moving from supervised or imitation learning contexts to learning a policy directly through RL, signifying the higher demands of RL environments.
3. Deterministic Systems: Remarkably, the presented lower bounds apply even under deterministic transition systems, where exploration challenges are traditionally mitigated.

Methodology

The researchers underpin their claims by constructing complex theoretical models that simulate RL tasks with varying representation capabilities. By employing sophisticated mathematical proofs, including the development of barycentric spanners and leveraging properties such as the approximate rank, they systematically show that even theoretically ideal representations may not suffice for sample-efficient learning under certain constraints — a finding that may surprise practitioners accustomed to thinking of good representations as a panacea.

Implications and Future Directions

This paper expansively extends the understanding of the interplay between representation quality and sample efficiency in RL. Practically, it advises caution in assuming that improved feature representations automatically translate into more efficient RL. Moreover, it challenges researchers to consider not only representational quality but also the broader structural and algorithmic ecosystem within which RL operates.

Given the potential for exponential sample complexity, the implications for the design of RL algorithms are immense. Future AI research could focus on discovering novel techniques or assumptions that alleviate the difficulties highlighted by this work, potentially leading to more scalable and robust RL systems. Furthermore, exploring new function approximation paradigms that better harness representations could be a fruitful area of investigation.

In sum, this research illuminates the essential consideration that while a solid representation is undeniably pivotal, it is not always sufficient for efficient learning in RL. Addressing these shortcomings requires sophisticated approaches that adeptly balance the nuanced demands of learning, exploration, and representation.