Behavior Cloning Under PD Control: A Finite-Horizon Theory of Gain-Dependent Error Amplification

Position controllers have become the dominant interface for executing learned manipulation policies. Yet a critical design decision remains understudied: how should we choose controller gains for policy learning? The conventional wisdom is to select gains based on desired task compliance or stiffness. However, this logic breaks down when controllers are paired with state-conditioned policies: effective stiffness emerges from the interplay between learned reactions and control dynamics, not from gains alone. We argue that gain selection should instead be guided by learnability: how amenable different gain settings are to the learning algorithm in use. In this work, we systematically investigate how position controller gains affect three core components of modern robot learning pipelines: behavior cloning, reinforcement learning from scratch, and sim-to-real transfer. Through extensive experiments across multiple tasks and robot embodiments, we find that: (1) behavior cloning benefits from compliant and overdamped gain regimes, (2) reinforcement learning can succeed across all gain regimes given compatible hyperparameter tuning, and (3) sim-to-real transfer is harmed by stiff and overdamped gain regimes. These findings reveal that optimal gain selection depends not on the desired task behavior, but on the learning paradigm employed. Project website: https://younghyopark.me/tune-to-learn

Neural behavior cloning compresses demonstrations into large models, making individual actions difficult to trace and policy updates costly. Retrieval policies retain access to demonstrations but struggle with mismatch between recorded and live behavior. We introduce Behavior Predictive Control (BPC), which synthesizes policies without end-to-end policy training by combining an action-aware retrieval metric, a Hankel-based action-continuation prior, and a closed-form one-step residual correction. Inspired by behavioral systems theory, BPC predicts future actions by blending stored observation-action data that best reconstructs the recent runtime observation--action history. Across simulated benchmarks and real-robot deployments, BPC is competitive with learned policies such as $π_{0.5}$ (surpassing it in some cases), while reducing policy fitting from hours to seconds on consumer GPUs and supporting closed-loop control upwards of 75 Hz on a Jetson Orin Nano. The retrieved demonstration windows and their coefficients also provide an intrinsic estimate of task progress. Retaining demonstrations within the deployed policy makes its predictions traceable to supporting trajectories and enables behavior revision through the demonstration bank.

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.