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Corpus ID: 222132883

No quantum speedup over gradient descent for non-smooth convex optimization

@article{Garg2020NoQS,
title={No quantum speedup over gradient descent for non-smooth convex optimization},
author={Ankit Garg and Robin Kothari and Praneeth Netrapalli and Suhail Sherif},
journal={ArXiv},
year={2020},
volume={abs/2010.01801}
}

We study the first-order convex optimization problem, where we have black-box access to a (not necessarily smooth) function $f:\mathbb{R}^n \to \mathbb{R}$ and its (sub)gradient. Our goal is to find an $\epsilon$-approximate minimum of $f$ starting from a point that is distance at most $R$ from the true minimum. If $f$ is $G$-Lipschitz, then the classic gradient descent algorithm solves this problem with $O((GR/\epsilon)^{2})$ queries. Importantly, the number of queries is independent of the… CONTINUE READING