📝 SummarXiv

Abstract

We present an algorithm for learning unknown parametric constraints from locally-optimal input-output trajectory data. We assume that the given data is generated by demonstrators with stochastic nonlinear dynamics who execute a state or output feedback law to robustly satisfy the constraints despite worst-case dynamics and output noise. We encode the Karush-Kuhn-Tucker (KKT) conditions of this robust optimal output feedback control problem within a feasibility problem to recover constraints consistent with the local optimality of the demonstrations. We prove that our constraint learning method (i) accurately recovers the demonstrator's state or output feedback policy, and (ii) conservatively estimates the set of all state or output feedback policies that ensure constraint satisfaction despite worst-case noise realizations. Moreover, we perform sensitivity analysis, proving that when demonstrations are corrupted by transmission error, the inaccuracy in the learned state or output feedback law scales linearly in the error magnitude. Our method accurately recovers unknown constraints from simulated noisy, closed-loop demonstrations generated using dynamics, both linear and nonlinear, (e.g., unicycle and quadrotor) and a range of state and output feedback mechanisms.