Quantum speedups for stochastic optimization
Quantum Physics
2024-07-26 v2 Data Structures and Algorithms
Optimization and Control
Abstract
We consider the problem of minimizing a continuous function given quantum access to a stochastic gradient oracle. We provide two new methods for the special case of minimizing a Lipschitz convex function. Each method obtains a dimension versus accuracy trade-off which is provably unachievable classically and we prove that one method is asymptotically optimal in low-dimensional settings. Additionally, we provide quantum algorithms for computing a critical point of a smooth non-convex function at rates not known to be achievable classically. To obtain these results we build upon the quantum multivariate mean estimation result of Cornelissen et al. 2022 and provide a general quantum-variance reduction technique of independent interest.
Cite
@article{arxiv.2308.01582,
title = {Quantum speedups for stochastic optimization},
author = {Aaron Sidford and Chenyi Zhang},
journal= {arXiv preprint arXiv:2308.01582},
year = {2024}
}