Sample-Efficient "Clustering and Conquer" Procedures for Parallel Large-Scale Ranking and Selection

This work aims to improve the sample efficiency of parallel large-scale ranking and selection (R&S) problems by leveraging correlation information. We modify the commonly used "divide and conquer" framework in parallel computing by adding a correlation-based clustering step, transforming it into "clustering and conquer". Theoretically, we develop a novel gradient-based analysis framework and show that this seemingly simple modification substantially improves the performance of large-scale R&S procedures. Our approach enjoys two key advantages: (1) it does not require highly accurate correlation estimation or precise clustering, and (2) it can be seamlessly integrated with various existing fixed-precision and fixed-budget R&S procedures while achieving optimal sample complexity. We also introduce a new parallel clustering algorithm tailored to large-scale settings. Finally, in large-scale AI applications such as neural architecture search, our methods demonstrate superior performance.