Quantum Algorithm for Online Exp-concave Optimization

• URL: http://arxiv.org/abs/2410.19688v1
• Date: Fri, 25 Oct 2024 16:58:44 GMT
• Title: Quantum Algorithm for Online Exp-concave Optimization
• Authors: Jianhao He, Chengchang Liu, Xutong Liu, Lvzhou Li, John C. S. Lui,
• Abstract summary: We present quantum online quasi-Newton methods to tackle the problem. Our method approximates the Hessian by quantum estimated inexact gradient. Such regret improves the optimal classical algorithm by a factor of $T2/3$.
• Score: 30.962392035110135
• License:
• Abstract: We explore whether quantum advantages can be found for the zeroth-order feedback online exp-concave optimization problem, which is also known as bandit exp-concave optimization with multi-point feedback. We present quantum online quasi-Newton methods to tackle the problem and show that there exists quantum advantages for such problems. Our method approximates the Hessian by quantum estimated inexact gradient and can achieve $O(n\log T)$ regret with $O(1)$ queries at each round, where $n$ is the dimension of the decision set and $T$ is the total decision rounds. Such regret improves the optimal classical algorithm by a factor of $T^{2/3}$.

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