Zeroth-order methods achieve the same expected convergence rate as first-order methods without extra dimension dependence by treating them as input-to-state stable systems with controllable perturbations.
Hessian- aware zeroth-order optimization for black-box adversarial attack.arXiv preprint arXiv:1812.11377
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From Cursed to Competitive: Closing the ZO-FO Gap via Input-to-State Stability
Zeroth-order methods achieve the same expected convergence rate as first-order methods without extra dimension dependence by treating them as input-to-state stable systems with controllable perturbations.