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Joint Lower Bounds for Zeroth-Order Nonconvex Optimization on Euclidean Balls

Zhang, Haihan et al.
arXiv (All) · Papers
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optimization-and-control
We prove a joint stochastic zeroth-order lower bound for Goldstein stationarity on a Euclidean query ball, even when the ball is guaranteed to contain a stationary point. In dimension $d$, let $f=\mathbb{E}[F(\cdot;ξ)]$, assume $\mathbb{E}[\operatorname{Lip}(F(\cdot;ξ))^2]\le L_0^2$, and bound the i
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