When Does Predictive Inverse Dynamics Outperform Behavior Cloning?

Behavior cloning (BC) is a practical offline imitation learning method, but it often fails when expert demonstrations are limited. Recent works have introduced a class of architectures named predictive inverse dynamics models (PIDMs) that combine a future-state predictor with an inverse dynamics model. While PIDMs often outperform BC, the reasons behind their benefits remain unclear. In this paper, we provide a theoretical explanation: PIDMs introduce a tradeoff. Conditioning the IDM on the predicted future state can significantly reduce variance, but the prediction itself introduces additional bias and variance. We establish conditions for PIDMs to achieve higher sample efficiency and lower prediction error than BC, with the gap widening when additional data sources are available. We validate the theoretical insights empirically in 2D navigation tasks, where BC requires up to five times (three times on average) more demonstrations than PIDM to reach comparable performance. Results are also illustrated in a complex 3D environment in a modern video game with high-dimensional visual inputs and stochastic transitions, where BC requires over 66\% more samples than PIDM.