On the Identifiability of Latent Action Policies

2025-10-01

AI Summary

This work addresses the identifiability problem of learning action representations from video data in Latent Action Policy Optimization (LAPO). Existing methods lack theoretical guarantees for recovering meaningful action representations. We formally define sufficient conditions for identifiability of latent action representations and prove that, under mild assumptions, the entropy-regularized LAPO objective uniquely recovers action representations satisfying desirable properties—including discreteness, causal interpretability, and statistical robustness. Our analysis reveals that entropy regularization implicitly imposes structural constraints on the action policy distribution, thereby resolving representation ambiguity—a key mechanism underlying the empirical success of discrete action representations. By integrating information-theoretic principles with statistical learning theory, this work establishes the first identifiability guarantee for unsupervised action representation learning, filling a foundational theoretical gap in LAPO.

Technology Category

• Knowledge Representation and Reasoning: Action, Change, and Causality
• Reasoning under Uncertainty: Uncertainty Representations
• Search and Optimization: Learning to Search

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

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.

Problem

• Studies identifiability of latent action policy learning from videos
• Analyzes statistical benefits and sources of unidentifiability in action representations
• Proves entropy-regularized objective identifies valid action representations

Innovation

• Identifies latent action policies from video data
• Proves entropy-regularized objective enables identifiability
• Explains benefits of discrete action representations