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We propose a theoretical framework for studying behavior cloning of complexexpert demonstrations using generative modeling. Our framework invokeslow-level controllers - either learned or implicit in position-command control- to stabilize imitation around expert demonstrations. We show that with (a) asuitable low-level stability guarantee and (b) a powerful enough generativemodel as our imitation learner, pure supervised behavior cloning can generatetrajectories matching the per-time step distribution of essentially arbitraryexpert trajectories in an optimal transport cost. Our analysis relies on astochastic continuity property of the learned policy we call "total variationcontinuity" (TVC). We then show that TVC can be ensured with minimaldegradation of accuracy by combining a popular data-augmentation regimen with anovel algorithmic trick: adding augmentation noise at execution time. Weinstantiate our guarantees for policies parameterized by diffusion models andprove that if the learner accurately estimates the score of the(noise-augmented) expert policy, then the distribution of imitator trajectoriesis close to the demonstrator distribution in a natural optimal transportdistance. Our analysis constructs intricate couplings between noise-augmentedtrajectories, a technique that may be of independent interest. We conclude byempirically validating our algorithmic recommendations, and discussingimplications for future research directions for better behavior cloning withgenerative modeling.

Provable Guarantees for Generative Behavior Cloning: Bridging Low-Level Stability and High-Level Behavior