Understanding Behavior Cloning with Action Quantization

2026-03-20

AI Summary

This work addresses the theoretical foundations of action quantization in behavioral cloning, where continuous actions are commonly discretized yet the implications of quantization error—particularly its temporal propagation and relationship to sample complexity—remain poorly understood. The paper establishes the first theoretical guarantees for behavioral cloning under action quantization by integrating autoregressive modeling, log-loss optimization, and dynamical stability analysis. It proposes a model-augmentation approach that relaxes conventional smoothness assumptions on the expert policy and characterizes the conditions under which different quantization schemes are effective. The analysis proves that quantized behavioral cloning can achieve optimal sample complexity, with quantization error inducing only polynomial temporal dependence, and further reveals a fundamental joint trade-off between quantization precision and statistical complexity.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Behavior cloning is a fundamental paradigm in machine learning, enabling policy learning from expert demonstrations across robotics, autonomous driving, and generative models. Autoregressive models like transformer have proven remarkably effective, from large language models (LLMs) to vision-language-action systems (VLAs). However, applying autoregressive models to continuous control requires discretizing actions through quantization, a practice widely adopted yet poorly understood theoretically. This paper provides theoretical foundations for this practice. We analyze how quantization error propagates along the horizon and interacts with statistical sample complexity. We show that behavior cloning with quantized actions and log-loss achieves optimal sample complexity, matching existing lower bounds, and incurs only polynomial horizon dependence on quantization error, provided the dynamics are stable and the policy satisfies a probabilistic smoothness condition. We further characterize when different quantization schemes satisfy or violate these requirements, and propose a model-based augmentation that provably improves the error bound without requiring policy smoothness. Finally, we establish fundamental limits that jointly capture the effects of quantization error and statistical complexity.

Problem

• behavior cloning
• action quantization
• autoregressive models
• sample complexity
• quantization error

Innovation

• behavior cloning
• action quantization
• autoregressive models
• sample complexity
• quantization error