Pessimistic Model-based Offline Reinforcement Learning under Partial Coverage (2107.06226v4)

Abstract: We study model-based offline Reinforcement Learning with general function approximation without a full coverage assumption on the offline data distribution. We present an algorithm named Constrained Pessimistic Policy Optimization (CPPO)which leverages a general function class and uses a constraint over the model class to encode pessimism. Under the assumption that the ground truth model belongs to our function class (i.e., realizability in the function class), CPPO has a PAC guarantee with offline data only providing partial coverage, i.e., it can learn a policy that competes against any policy that is covered by the offline data. We then demonstrate that this algorithmic framework can be applied to many specialized Markov Decision Processes where additional structural assumptions can further refine the concept of partial coverage. Two notable examples are: (1) low-rank MDP with representation learning where the partial coverage condition is defined using a relative condition number measured by the unknown ground truth feature representation; (2) factored MDP where the partial coverage condition is defined using density ratio based concentrability coefficients associated with individual factors.

• The paper introduces CPPO, a novel algorithm that uses pessimism to mitigate overfitting in offline reinforcement learning with partial data coverage.
• It leverages structured MDPs and representation learning to achieve competitive performance with polynomial sample complexity.
• The approach offers practical benefits for high-stakes applications like healthcare and autonomous driving where full data coverage is impractical.

Overview of "Pessimistic Model-based Offline Reinforcement Learning under Partial Coverage"

The paper "Pessimistic Model-Based Offline Reinforcement Learning under Partial Coverage" explores advancements in offline reinforcement learning (RL), focusing on model-based approaches. The authors Masatoshi Uehara and Wen Sun of Cornell University propose an algorithm named Constrained Pessimistic Policy Optimization (CPPO). This method leverages a general function class and employs constraints to incorporate pessimism, a mechanism that helps mitigate overfitting to the offline dataset, which may not cover the entire state-action space.

The key contribution of this work is the ability of CPPO to effectively learn policies using offline data that provides only partial coverage. Partial coverage implies that the dataset does not necessarily contain information about all possible actions in all states, but only about a subset of them. The proposed algorithm demonstrates this capacity while maintaining polynomial sample complexity. This is significant as it reduces the dependency on the exhaustive and impractical assumption that the offline dataset must cover the full spectrum of states and actions necessary for optimal policy determination.

One of the innovative aspects of this research is the adaptability of CPPO to various Markov Decision Processes (MDPs) structures. For instance, the method capitalizes on the properties of low-rank MDPs and exploits representation learning to handle scenarios with partial coverage more efficiently. The concept of relative condition number is introduced, measured via the unknown, intrinsic ground truth feature representations, offering a refined framework to define partial coverage in these structured environments.

Furthermore, the paper branches into the Bayesian setting to enhance offline RL methods. The Bayesian approach facilitates learning without explicitly constructing pessimism or reward penalties, which is notably challenging in intricate models. The authors propose a posterior sampling-based incremental policy optimization algorithm (PS-PO). This algorithm iteratively refines the policy using models sampled from a posterior distribution, showcasing the ability to find nearly optimal policies under partial coverage with polynomial sample complexity on expectation.

Numerical Results and Claims

The authors support their theoretical advancements with rigorous numerical results. CPPO achieves competitive performance despite partial coverage scenarios by ensuring that any comparator policy that the offline data covers is effectively learned. The notion of model-based concentrability coefficients, like $C^{\dagger}_{\pi^{*}}$, introduces an innovative tool to quantify and leverage partial coverage, extending the practical usability of the algorithm across diverse and structured MDPs.

Implications and Future Directions

The research conducted broadens the horizons of offline RL, emphasizing model-based methods' flexibility and potential superiority over model-free counterparts under partial coverage assumptions. The authors effectively argue that realizability in a model-based setting, which involves the model's ability to adequately represent the environment dynamics, is less restrictive compared to model-free settings which often necessitate stronger presumptions such as BeLLMan completeness.

The research poses implications for practical applications where full data coverage is unattainable, such as healthcare and autonomous driving, where exploratory actions might be costly or unsafe.

Looking ahead, this research suggests promising directions for future AI developments, particularly in building upon the adaptability and efficiency of model-based RL. Questions remain open for enhanced computational strategies, such as integrating posterior sampling in high-dimensional spaces efficiently, which could eventually lead to broader applicability and accelerated adoption in practical systems.

Conclusively, Uehara and Sun’s work signifies a pivotal step in leveraging pessimism in model-based offline RL, offering a comprehensive framework to handle partial coverage issues compellingly. This paper serves as a strong foundation for future research and development of robust, efficient, and practical RL algorithms in challenging real-world scenarios.