Unraveling the Hidden Dynamical Structure in Recurrent Neural Policies

TL;DR

This paper reveals that recurrent neural policies develop stable cyclic structures akin to limit cycles in dynamical systems, which explain their robustness, memory stabilization, and behavioral adaptability in control and meta-RL tasks.

Contribution

It uncovers the emergence of limit cycle structures in recurrent policies and links their geometry to policy behavior, offering new insights into their generalization capabilities.

Findings

Stable cyclic structures emerge in recurrent policies.

Limit cycle geometry correlates with policy behaviors.

Limit cycles stabilize memory and environmental states.

Abstract

Recurrent neural policies are widely used in partially observable control and meta-RL tasks. Their abilities to maintain internal memory and adapt quickly to unseen scenarios have offered them unparalleled performance when compared to non-recurrent counterparts. However, until today, the underlying mechanisms for their superior generalization and robustness performance remain poorly understood. In this study, by analyzing the hidden state domain of recurrent policies learned over a diverse set of training methods, model architectures, and tasks, we find that stable cyclic structures consistently emerge during interaction with the environment. Such cyclic structures share a remarkable similarity with \textit{limit cycles} in dynamical system analysis, if we consider the policy and the environment as a joint hybrid dynamical system. Moreover, we uncover that the geometry of such limit cycles also has a structured correspondence with the policies' behaviors. These findings offer new perspectives to explain many nice properties of recurrent policies: the emergence of limit cycles stabilizes both the policies' internal memory and the task-relevant environmental states, while suppressing nuisance variability arising from environmental uncertainty; the geometry of limit cycles also encodes relational structures of behaviors, facilitating easier skill adaptation when facing non-stationary environments.