On the Identifiability of Latent Action Policies

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 partly explains why discrete action representations are crucial in practice.