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

• URL: http://arxiv.org/abs/2307.14619v5
• Date: Tue, 24 Oct 2023 17:16:16 GMT
• Title: Provable Guarantees for Generative Behavior Cloning: Bridging Low-Level Stability and High-Level Behavior
• Authors: Adam Block, Ali Jadbabaie, Daniel Pfrommer, Max Simchowitz, Russ Tedrake
• Abstract summary: We propose a theoretical framework for studying behavior cloning of complex expert demonstrations using generative modeling. We show that pure supervised cloning can generate trajectories matching the per-time step distribution of arbitrary expert trajectories.
• Score: 51.60683890503293
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a theoretical framework for studying behavior cloning of complex expert demonstrations using generative modeling. Our framework invokes low-level controllers - either learned or implicit in position-command control - to stabilize imitation around expert demonstrations. We show that with (a) a suitable low-level stability guarantee and (b) a powerful enough generative model as our imitation learner, pure supervised behavior cloning can generate trajectories matching the per-time step distribution of essentially arbitrary expert trajectories in an optimal transport cost. Our analysis relies on a stochastic continuity property of the learned policy we call "total variation continuity" (TVC). We then show that TVC can be ensured with minimal degradation of accuracy by combining a popular data-augmentation regimen with a novel algorithmic trick: adding augmentation noise at execution time. We instantiate our guarantees for policies parameterized by diffusion models and prove that if the learner accurately estimates the score of the (noise-augmented) expert policy, then the distribution of imitator trajectories is close to the demonstrator distribution in a natural optimal transport distance. Our analysis constructs intricate couplings between noise-augmented trajectories, a technique that may be of independent interest. We conclude by empirically validating our algorithmic recommendations, and discussing implications for future research directions for better behavior cloning with generative modeling.

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