Self-Predictive Representations for Combinatorial Generalization in Behavioral Cloning

While goal-conditioned behavior cloning (GCBC) methods can perform well on in-distribution training tasks, they do not necessarily generalize zero-shot to tasks that require conditioning on novel state-goal pairs, i.e. combinatorial generalization. In part, this limitation can be attributed to a lack of temporal consistency in the state representation learned by BC; if temporally correlated states are properly encoded to similar latent representations, then the out-of-distribution gap for novel state-goal pairs would be reduced. We formalize this notion by demonstrating how encouraging long-range temporal consistency via successor representations (SR) can facilitate generalization. We then propose a simple yet effective representation learning objective, $\text{BYOL-}\gamma$ for GCBC, which theoretically approximates the successor representation in the finite MDP case through self-predictive representations, and achieves competitive empirical performance across a suite of challenging tasks requiring combinatorial generalization.