Title: EqR: Equivariant Representations for Data-Efficient Reinforcement Learning. Abstract: We study different notions of equivariance as an inductive bias in Reinforcement Learning (RL) and propose new mechanisms for recovering representations that are equivariant to both an agent’s action, and symmetry transformations of the state-action pairs. Whereas prior work on exploiting symmetries in deep RL can only incorporate predefined linear transformations, our approach allows for non-linear symmetry transformations of state-action pairs to be learned from the data itself. This is achieved through an equivariant Lie algebraic parameterization of state and action encodings, equivariant latent transition models, and the use of symmetry-based losses. We demonstrate the advantages of our learned equivariant representations for Atari games, in a data-efficient setting limited to 100k steps of interactions with the environment. Our method, which we call Equivariant representations for RL (EqR), outperforms many previous methods in a similar setting by achieving a median human-normalized score of 0.418, and surpassing human-level performance on 8 out of the 26 games.