Provable Guarantees for Generative Behavior Cloning: Bridging Low-Level Stability and High-Level Behavior (2307.14619v5)

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.

• The paper introduces a hierarchical framework that synthesizes simple controllers for localized stability in imitation learning.
• It employs a novel noise-injection strategy using Gaussian perturbations to ensure Total Variation Continuity and robust policy interpolation.
• Theoretical reductions demonstrate that generative cloning reliably approximates expert trajectories with polynomial sample complexity bounds.

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

The paper introduces a theoretical framework for generative behavior cloning within the context of complex expert demonstrations, leveraging low-level controller stability and powerful generative models. This research provides an extensive analysis of how imitation learning can effectively reproduce expert behaviors by implementing hierarchical control structures and data augmentation techniques in policy learning.

Key Contributions

1. Hierarchical Approach: The paper proposes a multi-layered framework that imitates sequences of simplified low-level feedback controllers, referred to as "primitive controllers." This approach allows for local stabilization around each expert trajectory, facilitating imitation learning in dynamic environments. The research underscores that synthesizing these controllers during training significantly contributes to reducing imitation error.
2. Novel Data Noise-Addition Strategy: The paper introduces a novel methodology of applying Gaussian noise to training data-inputs and reintroducing the same noise during the test time. This noise-injection aids in achieving what the authors term as "Total Variation Continuity" (TVC), a critical component that helps the learned policy interpolate effectively across distribution modes, thereby ensuring broad generalization while avoiding deterministic mode-switching.
3. Theoretical Assurance and Reductions: It presents reductions from a challenging conditional action sampling problem to approximating generative distribution learning. By defining conditions under which generative behavior cloning performs optimally, it bridges the gap between dynamic behavior cloning and supervised learning, thus implying broader applicability to complex trajectory-based demonstrations.
4. Implications for Generative Learning Models: By leveraging score-matching techniques familiar to Denoising Diffusion Probabilistic Models (DDPMs), the paper theoretically supports the feasibility of complex expert trajectory imitation by ensuring sample complexity remains polynomially bounded concerning relevant problem parameters, thus providing practical assurance of its efficacy.

Implications for Future Research

Theoretical Impacts: This work offers strong guarantees for behavior cloning with offline data, providing new directions in extending imitation learning beyond single-modal behaviors. The proposed TVC framework sets a foundation for ensuring continuity in probabilistic policy spaces, vital for real-time adaptive systems in robotics.

Practical Contributions: The employment of primitive controllers in generative models of imitation learning aligns well with practical dynamics in robotics and control systems, where multistage feedback laws and stabilization techniques are prevalent. The paper suggests practical tools, such as Ricatti-based synthesis and possibly novel hierarchical feedback designs suitable for nonlinear and smooth systems, greatly aiding practical deployments without necessitating heavy computational planning resources.

Experimental Validation and Future Directions

The proposed concepts are empirically tested in robotics simulation environments, demonstrating significant advancements over conventional imitation learning strategies. The empirical results reveal notable improvements in learning complex behaviors from limited demonstrations when primitive controllers are synthesized.

Future research might examine extending this hierarchical and stabilizatory approach to non-smooth or contact-dynamic systems, which commonly appear in more realistic robotic interaction scenarios. Additionally, further innovation could involve integrating these strategies with time-invariant policies, expanding their general applicability across various task dimensions and environments with fewer stabilization assumptions.

Overall, this work advances our understanding and capability to simulate expert behaviors under complex and dynamically evolving conditions, setting a promising trajectory for future developments in adaptive systems and autonomous agents.