提出随机零阶优化方法，高效求解一类特殊凸函数的最优点。
Minimisation of Quasar-Convex Functions Using Random Zeroth-Order Oracles
- 用高斯平滑处理无梯度信息的优化问题
- 证明算法在有约束下仍能收敛到全局最优邻域
- 适用于系统识别与广义线性模型等实际场景
本文研究了随机高斯平滑零阶（ZO）算法在无约束和有约束情形下对拟凸（QC）及强拟凸（SQC）函数的最小化性能。在无约束情况下，建立了算法对QC与SQC函数的收敛性及其复杂度；在有约束情况下，提出了新的近似拟凸性概念，并证明了类似结果：在方差缩减机制下，算法可收敛至全局最小值的可控邻域。此外，通过多个机器学习问题验证了理论结果的实际意义，包括线性动态系统识别与广义线性模型。
原文摘要 · Abstract (English)
This paper explores the performance of a random Gaussian smoothing zeroth-order (ZO) scheme for minimising quasar-convex (QC) and strongly quasar-convex (SQC) functions in both unconstrained and constrained settings. For the unconstrained problem, we establish the ZO algorithm's convergence to a global minimum along with its complexity when applied to both QC and SQC functions. For the constrained problem, we introduce the new notion of proximal-quasar-convexity and prove analogous results to the unconstrained case. Specifically, we derive complexity bounds and prove convergence of the algorithm to a neighbourhood of a global minimum whose size can be controlled under a variance reduction scheme. Beyond the theoretical guarantees, we demonstrate the practical implications of our results on several machine learning problems where quasar-convexity naturally arises, including linear dynamical system identification and generalised linear models.
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