Enhancing Batch Diversity in Surrogate Optimization: A Determinantal Point Processes Approach

The exploration–exploitation tradeoff poses a significant challenge in surrogate optimization for expensive black-box functions, particularly when dealing with batch evaluation settings. Despite efforts to develop batch sampling techniques, they often fall short of sufficiently prioritizing diversity within the selected batch. In this article, we propose a fundamentally novel approach called Determinantal Point Processes (DPP)-Based Surrogate Optimization (DPPSO), which serves as a consolidated framework. DPPSO introduces a novel discretization scheme and sampling algorithm that fuses exploration and exploitation objectives by harnessing the power of DPP decomposition. An essential aspect of this project is the development of effective scoring functions to incorporate the quality of the sampled points in the decomposition. We provide theoretical guarantees achieving lower bounds on the probability of convergence. We demonstrate the effectiveness of DPPSO across different benchmarks, comparing its performance against various baseline methods.