Provable Partially Observable Reinforcement Learning with Privileged Information (2412.00985v3)

Abstract: Partial observability of the underlying states generally presents significant challenges for reinforcement learning (RL). In practice, certain \emph{privileged information}, e.g., the access to states from simulators, has been exploited in training and has achieved prominent empirical successes. To better understand the benefits of privileged information, we revisit and examine several simple and practically used paradigms in this setting. Specifically, we first formalize the empirical paradigm of \emph{expert distillation} (also known as \emph{teacher-student} learning), demonstrating its pitfall in finding near-optimal policies. We then identify a condition of the partially observable environment, the \emph{deterministic filter condition}, under which expert distillation achieves sample and computational complexities that are \emph{both} polynomial. Furthermore, we investigate another useful empirical paradigm of \emph{asymmetric actor-critic}, and focus on the more challenging setting of observable partially observable Markov decision processes. We develop a belief-weighted asymmetric actor-critic algorithm with polynomial sample and quasi-polynomial computational complexities, in which one key component is a new provable oracle for learning belief states that preserve \emph{filter stability} under a misspecified model, which may be of independent interest. Finally, we also investigate the provable efficiency of partially observable multi-agent RL (MARL) with privileged information. We develop algorithms featuring \emph{centralized-training-with-decentralized-execution}, a popular framework in empirical MARL, with polynomial sample and (quasi-)polynomial computational complexities in both paradigms above. Compared with a few recent related theoretical studies, our focus is on understanding practically inspired algorithmic paradigms, without computationally intractable oracles.

• The paper analyzes provable partially observable RL methods leveraging privileged information, focusing on expert distillation and asymmetric actor-critic frameworks.
• The paper shows that privileged information under the deterministic filter condition allows polynomial sample and computational complexity in POMDPs, reducing prior exponential dependencies.
• The authors introduce a belief-weighted asymmetric actor-critic variant and extend the analysis to multi-agent POMDPs and function approximation.

An Analytical Examination of "Provable Partially Observable Reinforcement Learning with Privileged Information"

The paper "Provable Partially Observable Reinforcement Learning with Privileged Information" explores the intricate dynamics of partially observable reinforcement learning (RL) under the advantageous condition of additional or privileged information. The authors focus on the theoretical underpinning of empirical paradigms, particularly expert distillation and asymmetric actor-critic frameworks, while examining their utility in both traditional POMDPs and multi-agent settings.

Core Contributions and Theoretical Foundations

A principal contribution of this work is the formalization and analysis of expert distillation. Expert distillation, sometimes equated with teacher-student learning, involves transferring learned policies from environments where privileged information is available to settings without such advantages. The paper identifies potential pitfalls inherent in this approach, especially under generalized conditions lacking robust assumptions like deterministic filter conditions.

The deterministic filter condition serves as a central concept within the paper. This condition extends beyond deterministic POMDPs to include various subclasses like block MDPs and those with arbitrary decoding lengths. Under this condition, the paper establishes that both sample and computational complexities can be polynomial, contrary to previously known exponential dependencies in certain POMDP subclasses when privileged information is absent.

Asymmetric Actor-Critic: Analysis and Innovation

For the asymmetric actor-critic methodology, the authors tackle its inefficiency in observable POMDP settings using vanilla implementations. They introduce a belief-weighted asymmetric actor-critic variant. By incorporating belief state learning, the proposed method maintains filter stability even when the model is misspecified. This method achieves polynomial sample efficiency and quasi-polynomial computational complexity, demonstrating significant improvements over traditional methods.

Theoretical Implications and Practical Algorithms

The paper extends its investigation to multi-agent POMDPs, particularly emphasizing centralized training with decentralized execution (CTDE)—a prevalent framework in empirical multi-agent reinforcement learning. By leveraging privileged information during training, the authors provide algorithms that retain polynomial sample and quasi-polynomial computational complexities.

They also generalize their theoretical framework to function approximation settings, broadening its applicability to real-world scenarios with large observation spaces. Utilizing Daniely and Shalev-Shwartz-Dimension (DS Dimension) as a measure, the paper ensures PAC-learnability of multi-class classifiers, essential for handling extensive real-world applications.

Future Directions and Speculation

This work lays the groundwork for further exploration into partial observability within RL with potential expansions into biased or partially observable privileged information. Furthermore, extending these frameworks to environments characterized by continuous action spaces or high-dimensional settings remains a fertile field for exploration, particularly under function approximation paradigms.

Given that this paper synthesizes theoretical rigor with practical algorithmic strategies, its methodologies could apply broadly across robotics, autonomous systems, and beyond. Future work might explore integrating these findings into deep RL settings, potentially unveiling new facets of learning efficiency and decision-making in autonomous systems.

In conclusion, this paper advances our understanding of partially observable reinforcement learning by harnessing privileged information, offering a significant leap forward in both theoretical understanding and practical algorithm development. The rigorous analysis and innovative algorithmic contributions hold promise for enhancing the efficiency of learning processes in complex environments.