Reinforcement Learning under Latent Dynamics: Toward Statistical and Algorithmic Modularity (2410.17904v1)

Abstract: Real-world applications of reinforcement learning often involve environments where agents operate on complex, high-dimensional observations, but the underlying (''latent'') dynamics are comparatively simple. However, outside of restrictive settings such as small latent spaces, the fundamental statistical requirements and algorithmic principles for reinforcement learning under latent dynamics are poorly understood. This paper addresses the question of reinforcement learning under $\textit{general}$ latent dynamics from a statistical and algorithmic perspective. On the statistical side, our main negative result shows that most well-studied settings for reinforcement learning with function approximation become intractable when composed with rich observations; we complement this with a positive result, identifying latent pushforward coverability as a general condition that enables statistical tractability. Algorithmically, we develop provably efficient observable-to-latent reductions -- that is, reductions that transform an arbitrary algorithm for the latent MDP into an algorithm that can operate on rich observations -- in two settings: one where the agent has access to hindsight observations of the latent dynamics [LADZ23], and one where the agent can estimate self-predictive latent models [SAGHCB20]. Together, our results serve as a first step toward a unified statistical and algorithmic theory for reinforcement learning under latent dynamics.

• The paper demonstrates that naive function approximation fails in RL under latent dynamics, highlighting the need for modular statistical and algorithmic approaches.
• The study introduces statistical modularity via latent pushforward coverability, reducing complex observations to simpler latent state spaces.
• The paper proposes the O2L meta-algorithm, using hindsight observability and self-predictive learning to efficiently bridge observable and latent domains.

Reinforcement Learning under Latent Dynamics: Toward Statistical and Algorithmic Modularity

This paper addresses the intricacies of reinforcement learning (RL) in scenarios where complex, high-dimensional observations mask simple underlying latent dynamics. The paper focuses on understanding the statistical requirements and algorithmic principles needed when RL tasks are governed by these latent dynamics. The authors notably explore statistical and algorithmic modularity, offering insights for lifting known algorithms to operate effectively in these settings.

Contributions and Framework

The paper begins by framing RL in environments where agents contend with rich, high-dimensional observations that emanate from simpler latent dynamics. Recognizing that current literature predominantly grapples with limited settings, such as tabular state spaces, the authors introduce a generalized view of latent dynamics. This involves working with a latent state space and an emission process that maps these to the observable states. A pivotal point is made about the inadequacy of naive function approximation methods due to the intertwined nature of representation learning and exploration.

Statistical Modularity

A central theme is statistical modularity, which seeks to understand if the complexity of RL in latent dynamics can be reduced to the complexity of the latent state space. However, the paper provides a compelling negative result—most settings with function approximation lack statistical modularity, making them intractable when scaled with rich observations. Despite these significant challenges, the authors identify latent pushforward coverability as a structural property that can ensure statistical tractability.

Algorithmic Modularity

On the algorithmic front, the paper explores how RL under latent dynamics can be modularly approached by building reductions from the observable to the latent problem space. They propose the O2L meta-algorithm, capable of lifting any latent RL algorithm to the observable domain, given additional modeling assumptions are met. Specifically, the inclusion of hindsight observability and self-predictive representation learning are explored—methods where latent information is revealed post-decision, thereby aiding in representation learning.

Practical and Theoretical Implications

By bridging the gap between statistical and algorithmic challenges in RL under latent dynamics, this paper lays the groundwork for creating scalable RL algorithms that accommodate complex observations while leveraging latent simplicity. The statistical and algorithmic modularity frameworks provided could lead to new classes of RL algorithms that learn efficiently even with intricate observations, predicated upon the right latent structure assumptions.

Future Directions

The work highlights several open problems, such as determining the minimal requirements for computationally efficient representation learning, particularly in the absence of hindsight observability. It also poses questions about whether statistical modularity can fundamentally align with algorithmic modularity—with implications for developing universal machine learning frameworks.

In conclusion, this paper presents crucial advancements in understanding RL under latent dynamics, offering both theoretical insights and practical solutions. It sets a foundation for further research into modular RL solutions that effectively bridge the gap between rich observational data and the latent dynamics that govern them.