论文标题
改善较大维度的勘探策略和全球随机搜索算法的收敛速度
Improving exploration strategies in large dimensions and rate of convergence of global random search algorithms
论文作者
论文摘要
我们考虑全局优化问题，其中可行区域$ \ x $是$ \ mathbb {r}^d $的紧凑子集，带有$ d \ geq 10 $。对于这些问题，我们证明了以下内容。首先：基于随机点的渐近特性，全局随机搜索算法的实际收敛远比经典估计值的收敛速度要慢得多。第二：通常建议的空间探索方案在非肿瘤方面效率低下。具体而言，（a）整个〜$ \ x $上的均匀采样效率远低于$ \ x $的合适子集的均匀采样效率，而（b）通过低静态序列更换随机点的效果可忽略不计。
We consider global optimization problems, where the feasible region $\X$ is a compact subset of $\mathbb{R}^d$ with $d \geq 10$. For these problems, we demonstrate the following. First: the actual convergence of global random search algorithms is much slower than that given by the classical estimates, based on the asymptotic properties of random points. Second: the usually recommended space exploration schemes are inefficient in the non-asymptotic regime. Specifically, (a) uniform sampling on entire~$\X$ is much less efficient than uniform sampling on a suitable subset of $\X$, and (b) the effect of replacement of random points by low-discrepancy sequences is negligible.
