Perturbed gradient descent is small-disturbance input-to-state stable under a generalized nonlinear PL condition, and LQR policy gradient methods inherit this guarantee.
Robust accelerated gradient methods for smooth strongly convex functions
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Perturbed Gradient Descent Algorithms are Small-Disturbance Input-to-State Stable
Perturbed gradient descent is small-disturbance input-to-state stable under a generalized nonlinear PL condition, and LQR policy gradient methods inherit this guarantee.