[2603.20538] Understanding Behavior Cloning with Action Quantization

Computer Science > Machine Learning arXiv:2603.20538 (cs) [Submitted on 20 Mar 2026] Title:Understanding Behavior Cloning with Action Quantization Authors:Haoqun Cao, Tengyang Xie View a PDF of the paper titled Understanding Behavior Cloning with Action Quantization, by Haoqun Cao and 1 other authors View PDF HTML (experimental) 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 wit...