AI RESEARCH
A Nonasymptotic Theory of Gain-Dependent Error Dynamics in Behavior Cloning
arXiv CS.AI
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ArXi:2604.14484v1 Announce Type: cross Behavior cloning (BC) policies on position-controlled robots inherit the closed-loop response of the underlying PD controller, yet the effect of controller gains on BC failure lacks a nonasymptotic theory. We show that independent sub-Gaussian action errors propagate through the gain-dependent closed-loop dynamics to yield sub-Gaussian position errors whose proxy matrix $X_\infty(K)$ governs the failure tail.