  Offline reinforcement learning leverages large datasets to train policies
without interactions with the environment. The learned policies may then be
deployed in real-world settings where interactions are costly or dangerous.
Current algorithms over-fit to the training dataset and as a consequence
perform poorly when deployed to out-of-distribution generalizations of the
environment. We aim to address these limitations by learning a Koopman latent
representation which allows us to infer symmetries of the system's underlying
dynamic. The latter is then utilized to extend the otherwise static offline
dataset during training; this constitutes a novel data augmentation framework
which reflects the system's dynamic and is thus to be interpreted as an
exploration of the environments phase space. To obtain the symmetries we employ
Koopman theory in which nonlinear dynamics are represented in terms of a linear
operator acting on the space of measurement functions of the system and thus
symmetries of the dynamics may be inferred directly. We provide novel
theoretical results on the existence and nature of symmetries relevant for
control systems such as reinforcement learning settings. Moreover, we
empirically evaluate our method on several benchmark offline reinforcement
learning tasks and datasets including D4RL, Metaworld and Robosuite and find
that by using our framework we consistently improve the state-of-the-art of
model-free Q-learning methods.
