Web: http://arxiv.org/abs/2209.10346

Sept. 22, 2022, 1:11 a.m. | Guy Kornowski, Ohad Shamir

cs.LG updates on arXiv.org arxiv.org

We study the oracle complexity of producing $(\delta,\epsilon)$-stationary
points of Lipschitz functions, in the sense proposed by Zhang et al. [2020].
While there exist dimension-free randomized algorithms for producing such
points within $\widetilde{O}(1/\delta\epsilon^3)$ first-order oracle calls, we
show that no dimension-free rate can be achieved by a deterministic algorithm.
On the other hand, we point out that this rate can be derandomized for smooth
functions with merely a logarithmic dependence on the smoothness parameter.
Moreover, we establish several lower bounds …

arxiv complexity math optimization small

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