{"ID":2832613,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.05825","arxiv_id":"2512.05825","title":"Approximation of Box Decomposition Algorithm for Fast Hypervolume-Based Multi-Objective Optimization","abstract":"Hypervolume (HV)-based Bayesian optimization (BO) is one of the standard approaches for multi-objective decision-making. However, the computational cost of optimizing the acquisition function remains a significant bottleneck, primarily due to the expense of HV improvement calculations. While HV box-decomposition offers an efficient way to cope with the frequent exact improvement calculations, it suffers from super-polynomial memory complexity $O(MN^{\\lfloor \\frac{M + 1}{2} \\rfloor})$ in the worst case as proposed by Lacour et al. (2017). To tackle this problem, Couckuyt et al. (2012) employed an approximation algorithm. However, a rigorous algorithmic description is currently absent from the literature. This paper bridges this gap by providing comprehensive mathematical and algorithmic details of this approximation algorithm.","short_abstract":"Hypervolume (HV)-based Bayesian optimization (BO) is one of the standard approaches for multi-objective decision-making. However, the computational cost of optimizing the acquisition function remains a significant bottleneck, primarily due to the expense of HV improvement calculations. While HV box-decomposition offers...","url_abs":"https://arxiv.org/abs/2512.05825","url_pdf":"https://arxiv.org/pdf/2512.05825v1","authors":"[\"Shuhei Watanabe\"]","published":"2025-12-05T15:43:06Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\"]","methods":"[]","has_code":false}