We aim to efficiently allocate a fixed simulation budget to identify the top-mc designs for each context among a finite number of contexts. The performance of each design under a context is measured by an identifiable statistical characteristic, possibly with the existence of nuisance parameters. Under a Bayesian framework, we extend the top-two Thompson sampling method designed for selecting the best design in a single context to the contextual top-mc selection problems, leading to an efficient sampling policy that simultaneously allocates simulation samples to both contexts and designs. To demonstrate the asymptotic optimality of the proposed sampling policy, we characterize the exponential convergence rate of the posterior distribution for a wide range of identifiable sampling distribution families. The proposed sampling policy is proved to be consistent, and asymptotically satisfies a necessary condition for optimality. In particular, when selecting contextual best designs (i.e., mc = 1), the proposed sampling policy is proved to be asymptotically optimal. Numerical experiments demonstrate the good finite sample performance of the proposed sampling policy.

翻译：我们旨在高效分配有限的仿真预算，以在有限个上下文中识别每个上下文对应的Top-mc设计方案。每个设计方案在某个上下文下的性能由一个可识别的统计特征度量，该度量可能包含冗余参数。在贝叶斯框架下，我们将原本为单一上下文最优设计方案选择而设计的Top-Two Thompson采样方法扩展到上下文Top-mc选择问题，提出了一种同时将仿真样本分配给上下文和设计方案的高效采样策略。为证明所提采样策略的渐近最优性，我们刻画了广泛可识别采样分布族下后验分布的指数收敛速率。所提采样策略被证明具有一致性，并且渐近满足最优性的必要条件。特别地，当选择上下文最优设计方案（即mc=1）时，该采样策略被证明是渐近最优的。数值实验表明所提采样策略具有良好的有限样本性能。