Top-Two Thompson Sampling for Selecting Context-Dependent Best Designs

We consider a contextual ranking and selection problem which aims to identify the best-performing alternative for each context. The performance is measured by an arbitrary identifiable statistical characteristic. Under a Bayesian framework, we establish the posterior large deviation ratios for general adaptive sampling policies. We propose an efficient sampling policy based on top-two Thompson sampling, which is proven to be consistent. Numerical experiments demonstrate that the proposed algorithm outperforms existing algorithms under both Gaussian and non-Gaussian settings.