Dual-Directed Algorithm Design for Efficient Pure Exploration

We consider pure-exploration problems in the context of stochastic sequential adaptive experiments with a finite set of alternative options. The goal of the decision-maker is to accurately answer a query question regarding the alternatives with high confidence with minimal measurement efforts. A typical query question is to identify the alternative with the best performance, leading to ranking and selection problems, or best-arm identification in the machine learning literature. We focus on the fixed-precision setting and derive a sufficient condition for optimality in terms of a notion of strong convergence to the optimal allocation of samples. Using dual variables, we characterize the necessary and sufficient conditions for an allocation to be optimal. The use of dual variables allow us to bypass the combinatorial structure of the optimality conditions that relies solely on primal variables. Remarkably, these optimality conditions enable an extension of top-two algorithm design principle, initially proposed for best-arm identification. Furthermore, our optimality conditions give rise to a straightforward yet efficient selection rule, termed information-directed selection, which adaptively picks from a candidate set based on information gain of the candidates. We outline the broad contexts where our algorithmic approach can be implemented. We establish that, paired with information-directed selection, top-two Thompson sampling is (asymptotically) optimal for Gaussian best-arm identification, solving a glaring open problem in the pure exploration literature. Our algorithm is optimal for $\epsilon$-best-arm identification and thresholding bandit problems. Our analysis also leads to a general principle to guide adaptations of Thompson sampling for pure-exploration problems. Numerical experiments highlight the exceptional efficiency of our proposed algorithms relative to existing ones.Comment: An earlier version of this paper appeared as an extended abstract in the Proceedings of the 36th Annual Conference on Learning Theory, COLT'23, with the title "Information-Directed Selection for Top-Two Algorithms.'

A Survey From West of China: The Factors Affecting the Selection of College Students' Returning to Work in Their Hometowns

College graduates will be more important in the development of China. Chinese higher education has made great progress but fewer and fewer graduates are willing to return to a rural community. We developed a survey by 2013-2014 with western college students to find how factors are affecting college students’ work area. Students’ attitudes, college courses and family are the focus of this research. The interaction between attitudes and college lives, attitudes and family influence are discussed. The result shows that the college students hold a neutral attitude which has no significant sexual differences. The significance exists in ethnicity. There are significant correlations among 3 dimensions