单位立方体上球面线性贝叶斯优化的采集函数新方法
Acquisition for Spherical-Linear Bayesian Optimization on the Cube
这篇论文把贝叶斯优化的采集函数求解提速了，精度不输 GP 版本，做超参优化或实验设计的可以看看。
arXiv 论文 2610.32628 研究贝叶斯优化（BO）在单位立方体决策域上的采集子问题求解复杂度。现有方法用多起点拟牛顿法求解采集子问题，作者分析了全局求解的正负两方面复杂度结果。论文提出一种新的采集函数，可全局优化且执行时间明显低于现有方法。在黑盒函数上，该方法每次评估的精度与高斯过程（GP）版 BO 相当，在中低计算强度问题上单位墙钟时间的精度更高。
Acquisition for Spherical-Linear Bayesian Optimization on the Cube
Recent work demonstrated that executing Bayesian Optimization (BO) using simply a linear surrogate with a clever transformation is enough to approximate the performance of the standard Gaussian-Process (GP) based version on high-dimensional test functions. When the decision region is a sphere, this strategy admits rapid exact acquisition. However, it is the unit cube we encounter most often in the BO literature, and in this setting a standard approach, namely a multi-start quasi-Newton method, is employed for solving the acquisition subproblem. In this article, we will discuss a series of results, both positive and negative, regarding the complexity of global resolution of various acquisition subproblems over the unit cube. On the basis of this discussion, we will propose a new acquisition function which is globally optimizable using significantly less execution time than the incumbent approach while maintaining or improving performance. The resulting method is competitive with GP-based BO in terms of accuracy per evaluation, and is superior in terms of accuracy per walltime on black-boxes of low to moderate computational intensity.