Towards Robust Bisimulation Metric Learning

Learned representations in deep reinforcement learning (DRL) have to extract task-relevant information from complex observations, balancing between robustness to distraction and informativeness to the policy. Such stable and rich representations, often learned via modern function approximation techniques, can enable practical application of the policy improvement theorem, even in high-dimensional continuous state-action spaces. Bisimulation metrics offer one solution to this representation learning problem, by collapsing functionally similar states together in representation space, which promotes invariance to noise and distractors. In this work, we generalize value function approximation bounds for on-policy bisimulation metrics to non-optimal policies and approximate environment dynamics. Our theoretical results help us identify embedding pathologies that may occur in practical use. In particular, we find that these issues stem from an underconstrained dynamics model and an unstable dependence of the embedding norm on the reward signal in environments with sparse rewards. Further, we propose a set of practical remedies: (i) a norm constraint on the representation space, and (ii) an extension of prior approaches with intrinsic rewards and latent space regularization. Finally, we provide evidence that the resulting method is not only more robust to sparse reward functions, but also able to solve challenging continuous control tasks with observational distractions, where prior methods fail.