Quantum speedups for stochastic optimization

• URL: http://arxiv.org/abs/2308.01582v2
• Date: Thu, 25 Jul 2024 03:21:25 GMT
• Title: Quantum speedups for stochastic optimization
• Authors: Aaron Sidford, Chenyi Zhang,
• Abstract summary: We consider the problem of minimizing a continuous function given quantumvitzvariance to an oracle. We provide two new methods for the special case of minimizing a Lipsch avvitz function.
• Score: 18.32349609443295
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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