Is Pessimism Provably Efficient for Offline RL? (2012.15085v3)

Abstract: We study offline reinforcement learning (RL), which aims to learn an optimal policy based on a dataset collected a priori. Due to the lack of further interactions with the environment, offline RL suffers from the insufficient coverage of the dataset, which eludes most existing theoretical analysis. In this paper, we propose a pessimistic variant of the value iteration algorithm (PEVI), which incorporates an uncertainty quantifier as the penalty function. Such a penalty function simply flips the sign of the bonus function for promoting exploration in online RL, which makes it easily implementable and compatible with general function approximators. Without assuming the sufficient coverage of the dataset, we establish a data-dependent upper bound on the suboptimality of PEVI for general Markov decision processes (MDPs). When specialized to linear MDPs, it matches the information-theoretic lower bound up to multiplicative factors of the dimension and horizon. In other words, pessimism is not only provably efficient but also minimax optimal. In particular, given the dataset, the learned policy serves as the "best effort" among all policies, as no other policies can do better. Our theoretical analysis identifies the critical role of pessimism in eliminating a notion of spurious correlation, which emerges from the "irrelevant" trajectories that are less covered by the dataset and not informative for the optimal policy.

• The paper proposes the PEVI algorithm that integrates a pessimistic penalty in value estimation to counteract spurious correlations in offline RL.
• It decomposes policy suboptimality into factors like spurious correlation, intrinsic uncertainty, and optimization error, providing strong theoretical guarantees.
• PEVI achieves near-optimal performance in linear MDPs and demonstrates robust applicability in real-world scenarios where safe exploration is limited.

An Analytical Perspective on Pessimism in Offline Reinforcement Learning

The paper "Is Pessimism Provably Efficient for Offline RL?" by Ying Jin et al. addresses the challenge of offline reinforcement learning (RL) by proposing a Pessimistic Value Iteration (PEVI) algorithm, a variant of the classical value iteration, modified to incorporate pessimism in the estimation of action-value functions.

Motivation and Challenge

Offline RL is characterized by learning policies from fixed datasets collected without exploration, which inherently leads to challenges related to the insufficient coverage of state-action spaces. This data restriction often results in spurious correlations that misguide the learning algorithm, causing it to overestimate the values of poorly explored areas, thus complicating the learning of an optimal policy.

The Algorithmic Proposition

PEVI significantly hinges on flipping the bonus used for exploration in online RL into a penalty, effectively employing a pessimistic estimation of action-values conditioned on uncertainty. At its core, the approach utilizes a data-dependent penalty function, embedding an uncertainty quantifier that bounds the deviation of the estimated BeLLMan operator from its empirical counterpart, within a confidence range.

Theoretical Guarantees

1. Decomposition of Suboptimality: The researchers decompose a policy's suboptimality into spurious correlation, intrinsic uncertainty, and optimization error. They show that intrinsic uncertainty, the variation due to incomplete information, is inescapable and stems from finite sample effects, contributing to the fundamental bounds of any algorithm's capacity to learn optimal or near-optimal policies from offline data.
2. General MDP Settings: In establishing a data-dependent suboptimality bound for PEVI, the paper does not consider uniform coverage assumptions, focusing only on compliance, which means the offline data was generated under the same model dynamics as the learning model. This makes PEVI broadly applicable to real datasets with minimal theoretical prerequisites.
3. Linear MDPs: When specialized to linear Markov Decision Processes (MDPs), PEVI is shown to achieve near-optimal performance, aligning with the information-theoretic lower bound. The algorithm's suboptimality proportionally relates to the square root of the effective sample size in state-action visits along the optimal trajectory, underscoring the significance of the estimation accuracy along these critical states.

Information-Theoretic Lower Bounds

The derivation of a minimax lower bound affirms that PEVI is optimal within a multiplicative constant for linear MDPs, which contrasts with the requirements of comparable methods reliant on stronger assumptions or less practical conditions. Moreover, PEVI manifests the potential to exploit existing datasets better by establishing the trajectory coverage of the optimal policy, demonstrating potential beyond merely imitating demonstrated policies.

Challenges Addressed and Practical Implications

The PEVI algorithm is free from restrictions on the behavior policy, meaning it can achieve optimal or near-optimal results without depending on the similarity between the behavior policy (that generated data) and the learning target policy. This ability positions PEVI as a robust candidate for domains like autonomous driving or precision medicine where exploration is unsafe or infeasible. Moreover, the non-dependence on concentrated data coverage makes it attractive for real-world applications where data is collected passively.

Hypothetical Extensions

The flexibility of PEVI in not depending on particular transition dynamics or environment structures lays the groundwork for extensions to more expressive and structured function approximators, such as those utilized in state-of-the-art deep RL methods. By adapting the mechanism of uncertainty quantification through kernel methods or neural network embeddings, it is conceivable to extend the effectiveness of PEVI beyond the traditional settings evaluated in this paper.

In conclusion, the paper comprehensively evaluates the role of pessimism in offline RL, underpinning its efficiency with rigorous theoretical analysis, and providing a distinct direction for algorithmic developments that can overcome the inadequacies imposed by limited interaction data. Through these contributions, it paves the way for future explorations into function approximation and generalization in offline reinforcement settings.