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

This work breaks the sample efficiency bottleneck in parallel large-scale ranking and selection (R&S) problem 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". This seemingly simple modification can achieve an $\mathcal{O}(p)$ sample complexity reduction rate, which represents the maximum attainable reduction for the class of sample-optimal R&S methods. Our approach enjoys two key advantages: 1) it does not require highly accurate correlation estimation or precise clustering, and 2) it allows for seamless integration with various existing R&S method, while achieving optimal sample complexity. Theoretically, we develop a novel gradient analysis framework to analyze sample efficiency and guide the design of large-scale R&S procedures. Building upon this framework, we propose a gradient-based budget allocation policy. We also introduce a new clustering algorithm, selection policy, and precision criterion tailored for large-scale scenarios. Finally, in large-scale AI applications such as neural architecture search, our methods demonstrate superior performance.