Symmetry-Based Disentangled Representation Learning requires Interaction with Environments

Published in the proceedings of the Workshop on "Structure & Priors in Reinforcement Learning" at ICLR 2019 Finding a generally accepted formal definition of a disentangled representation in the context of an agent behaving in an environment is an important challenge towards the construction of data-efficient autonomous agents. Higgins et al. (2018) recently proposed Symmetry-Based Disentangled Representation Learning, a definition based on a characterization of symmetries in the environment using group theory. We build on their work and make observations, theoretical and empirical, that lead us to argue that Symmetry-Based Disentangled Representation Learning cannot only be based on fixed data samples. Agents should interact with the environment to discover its symmetries. All of our experiments can be reproduced on Colab: http://bit.do/eKpqv. Disentangled Representation Learning aims at finding a low-dimensional vectorial representation of the world for which the underlying structure of the world is separated into disjoint parts (i.e., disentangled) corresponding to the actual compositional nature of the world. Previous work (Raffin et al., 2019) has shown that agents capable of learning disentangled representations can perform dataefficient policy learning. However, there is no generally accepted formal definition of disentanglement in Representation Learning, which prevents significant progress in this emerging field.