We consider an expected-value ranking and selection (R&S) problem where all k solutions' simulation outputs depend on a common parameter whose uncertainty can be modeled by a distribution. We define the most probable best (MPB) to be the solution that has the largest probability of being optimal with respect to the distribution and design an efficient sequential sampling algorithm to learn the MPB when the parameter has a finite support. We derive the large deviations rate of the probability of falsely selecting the MPB and formulate an optimal computing budget allocation problem to find the rate-maximizing static sampling ratios. The problem is then relaxed to obtain a set of optimality conditions that are interpretable and computationally efficient to verify. We devise a series of algorithms that replace the unknown means in the optimality conditions with their estimates and prove the algorithms' sampling ratios achieve the conditions as the simulation budget increases. Furthermore, we show that the empirical performances of the algorithms can be significantly improved by adopting the kernel ridge regression for mean estimation while achieving the same asymptotic convergence results. The algorithms are benchmarked against a state-of-the-art contextual R&S algorithm and demonstrated to have superior empirical performances.
Best-Subset Selection in Generalized Linear Models: A Fast and Consistent Algorithm via Splicing Technique
Saw Swee Hock School of Public Health, National University of Singapore（新加坡国立大学杨潞龄公共卫生学院）；Southern China Center for Statistical Science, Department of Statistical Science, School of Mathematics, Sun Yat-Sen University（中山大学数学学院统计科学系华南统计科学研究中心）；Department of Statistics and Finance/International Institute of Finance, School of Management, University of Science and Technology of China（中国科学技术大学管理学院统计与金融系/国际金融研究院）；School of Statistics and Information, Shanghai University of International Business and Economics（上海对外经贸大学统计与信息学院）
