This research provides a theoretical foundation for behavior cloning using action quantization, a common practice in robotics and large-scale AI models where continuous signals are converted into discrete tokens. The authors analyze how quantization error and statistical complexity interact to influence a model’s performance over time. Their findings demonstrate that stable dynamics and smooth policies are essential for preventing small errors from compounding into significant failures. The study specifically highlights that binning-based quantization is more reliable than learning-based methods when imitating deterministic experts. To address potential instability, the paper proposes a model-based augmentation that improves accuracy without requiring high levels of policy smoothness. Finally, the researchers establish information-theoretic lower bounds to define the fundamental limits of learning from quantized demonstrations.