# Understanding Behavior Cloning with Action Quantization

arXiv: https://arxiv.org/abs/2603.20538 · HTML: https://mlsanity.com/paper/2603.20538/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 20 of its 38 references that are in the map.
- First posted on arXiv 20 Mar 2026.

## Placed in

- Offline RL and imitation learning from data / [Imitation learning methods](https://mlsanity.com/offlinerl/imitation-learning-methods/)

## Builds on (most cited first, 20 of 20)

- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Taming Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2012.09841/) (2020)
- [OpenVLA: An Open-Source Vision-Language-Action Model](https://mlsanity.com/paper/2406.09246/) (2024)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [π0: A Vision-Language-Action Flow Model for General Robot Control](https://mlsanity.com/paper/2410.24164/) (2024)
- [RT-1: Robotics Transformer for Real-World Control at Scale](https://mlsanity.com/paper/2212.06817/) (2022)
- [Learning Fine-Grained Bimanual Manipulation with Low-Cost Hardware](https://mlsanity.com/paper/2304.13705/) (2023)
- [Visual Autoregressive Modeling: Scalable Image Generation via Next-Scale Prediction](https://mlsanity.com/paper/2404.02905/) (2024)
- [FAST: Efficient Action Tokenization for Vision-Language-Action Models](https://mlsanity.com/paper/2501.09747/) (2025)
- [Behavior Generation with Latent Actions](https://mlsanity.com/paper/2403.03181/) (2024)
- [Knowledge Insulating Vision-Language-Action Models: Train Fast, Run Fast, Generalize Better](https://mlsanity.com/paper/2505.23705/) (2025)
- [Q-Transformer: Scalable Offline Reinforcement Learning via Autoregressive Q-Functions](https://mlsanity.com/paper/2309.10150/) (2023)
- [Toward the Fundamental Limits of Imitation Learning](https://mlsanity.com/paper/2009.05990/) (2020)
- [Is Behavior Cloning All You Need? Understanding Horizon in Imitation Learning](https://mlsanity.com/paper/2407.15007/) (2024)
- [QueST: Self-Supervised Skill Abstractions for Learning Continuous Control](https://mlsanity.com/paper/2407.15840/) (2024)
- [Provable Guarantees for Generative Behavior Cloning: Bridging Low-Level Stability and High-Level Behavior](https://mlsanity.com/paper/2307.14619/) (2023)
- [The Pitfalls of Imitation Learning when Actions are Continuous](https://mlsanity.com/paper/2503.09722/) (2025)
- [Continuous Control with Action Quantization from Demonstrations](https://mlsanity.com/paper/2110.10149/) (2021)
- [TaSIL: Taylor Series Imitation Learning](https://mlsanity.com/paper/2205.14812/) (2022)
- [Optimal Quantization for Matrix Multiplication](https://mlsanity.com/paper/2410.13780/) (2024)

## Abstract (arXiv)

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.