On the Identifiability of Latent Action Policies (2510.01337v1)

Abstract: We study the identifiability of latent action policy learning (LAPO), a framework introduced recently to discover representations of actions from video data. We formally describe desiderata for such representations, their statistical benefits and potential sources of unidentifiability. Finally, we prove that an entropy-regularized LAPO objective identifies action representations satisfying our desiderata, under suitable conditions. Our analysis provides an explanation for why discrete action representations perform well in practice.

• The paper presents key conditions ensuring that latent action policies are identifiable under an entropy-regularized objective.
• It outlines a methodology combining unsupervised state prediction, inverse dynamics modeling, and fine-tuning with minimal labeled data.
• The study demonstrates that enforcing determinism, disentanglement, and informativeness can robustly map latent actions, improving scalability.

Identifiability of Latent Action Policies

Introduction

The paper "On the Identifiability of Latent Action Policies" addresses the identifiability of latent action policy learning (LAPO), a recent framework designed to facilitate learning action representations from video data. LAPO seeks to minimize the reliance on action-annotated datasets by harnessing large volumes of unannotated video data. This necessitates a rigorous evaluation of the statistical properties of the learned representations, specifically focusing on their identifiability under entropy-regularized objectives.

Background and Framework

LAPO significantly reduces the dependency on expert-labeled action datasets by leveraging large amounts of unannotated video data. The LAPO process involves an initial unsupervised phase to predict state transitions, followed by labeling of latent actions using an inverse dynamics model (IDM). Finally, these latent representations are connected to real actions through fine-tuning with a smaller action-labeled dataset. The paper explores the statistical implications and identifiability of these representations, highlighting the importance of disentanglement and informativeness.

Data-Generating Process

In the given model, the environment the robot acts within is represented by a sequence of observations, and actions are discrete. Each action is contingent upon the state, and the transition model is deterministic. The identifiability analysis relies on these observations: firstly, the data-generating process must ensure separate influences of each action, and secondly, the model should maintain the continuity within the state space.

Desiderata and Statistical Efficiency

The paper delineates three desiderata for IDM: determinism, disentanglement, and informativeness. Determinism requires a unique mapping from a given state-action pair to a latent action. Disentanglement insists that the latent action's meaning must not depend on the informant state. Informativeness mandates that distinct ground-truth actions should map to distinct latent actions. If these conditions are met, the latent policy will closely approximate the expert policy in terms of learnability and transferability, thereby requiring fewer labeled training samples.

Entropy-Regularized LAPO Objective

An entropy-regularized LAPO objective is proposed to achieve deterministic encodings of actions. The hypothesis spaces for the forward and inverse dynamics models are defined, ensuring continuity in encoding and decoding actions. The population objective integrates these spaces ensuring minimal reconstruction loss while preserving the encoding's determinism and informativeness through regularization.

Unidentifiability Challenges

Potential sources of unidentifiability arise from misalignments between assumptions of the objective function and the observed data. Specifically, if the policy's action choices are deterministic or if the IDM is improperly constrained, the resulting representations may violate the desiderata, leading to ineffectiveness in capturing the true essence of the actions.

Main Results and Implications

The primary result establishes conditions under which the LAPO objective can guarantee identifiable representations adhering to the desiderata. Assumptions such as the continuity of the transition model, separation of distinct actions' effects, and their connected supports within the state space underpin these results. These findings also suggest that with careful application, LAPO can foster robust, scalable learning of latent action policies in scenarios with limited labeled data.

Figure 1: Illustration of the assumptions regarding connected supports and intersecting priors for identifiability.

Conclusion

This research systematically explores the foundational aspects of identifiability within the LAPO framework, providing a theoretical basis for their empirical application in AI systems using latent action representations. It suggests pathways to leverage unannotated data efficiently in learning algorithms, potentially impacting a wide range of real-world applications where action labeling is expensive or infeasible. Further research could expand on these results, addressing variances across different model architectures and data conditions.