先收敛后发散：解耦多目标贝叶斯优化中的收敛性与多样性
Converge Then Diversify: Decoupling Convergence and Diversity in Multi-Objective Bayesian Optimisation
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中文总结 AI 辅助
针对多目标贝叶斯优化中同时优化收敛与多样性的困难，提出先收敛后发散的两阶段方法，在紧张预算下显著优于现有方法。
中文摘要 AI 辅助
多目标贝叶斯优化（MOBO）是一种样本高效的方法，用于优化具有多个目标的昂贵黑箱函数。在MOBO中，目标是充分逼近帕累托前沿；即获得一个高质量的解决方案集，该集合需具备1）良好的收敛性（接近帕累托前沿）和2）良好的多样性（在帕累托前沿上的分布）。现有的MOBO方法通常旨在同时完成这两个任务，即驱动搜索朝向帕累托前沿，同时维持一组多样化的非支配解，使得解理想情况下能逐渐逼近整个前沿。当有足够的搜索预算时，这种方法有效。然而，在整个搜索过程中同时考虑收敛性和多样性并不容易，需要精心设计。在预算非常紧张的情况下，可能没有足够的解生成来同时逼近整个帕累托前沿。为解决此问题，本文提出了一种“先收敛后发散”（CTD）方法，将收敛性和多样性解耦为两个阶段。在第一阶段，CTD专注于收敛性，旨在快速驱动搜索朝向帕累托前沿上的单个点。在第二阶段，CTD专注于多样性，旨在将解分布到整个前沿。我们通过使用该领域广泛采用的采集函数，给出了CTD的两种简单实例化。实验结果表明，在所有446组成对比较中，CTD在72.9%的情况下统计上优于最先进方法，在21.1%的情况下表现相当，仅在6.1%的情况下统计上较差，其优势在评估预算非常紧张或高维问题的设置中尤为明显。
英文摘要
Multi-objective Bayesian optimisation (MOBO) is a sample-efficient approach for optimising expensive black-box functions with multiple objectives. In MOBO, the goal is to adequately approximate the Pareto front; that is, to obtain a high-quality solution set with 1) good convergence (closeness to the Pareto front) and 2) good diversity (spread across the Pareto front). Existing MOBO methods typically aim to accomplish these two tasks simultaneously, i.e., driving the search towards the Pareto front while maintaining a diverse set of nondominated solutions, such that the solutions, ideally, can gradually approach the entire front. When sufficient search budgets are available, this approach is effective. However, considering both convergence and diversity throughout the search is not easy and requires careful design. Under very tight budgets, there may not be enough solutions generated to be able to simultaneously approach the entire Pareto front. To address this issue, this paper proposes a \textit{converge-then-diversify} (CTD) approach that decouples convergence and diversity into two stages. In the first stage, CTD focuses on convergence, aiming to quickly drive the search toward a single point on the Pareto front. In the second stage, CTD focuses on diversity, aiming to spread solutions across the front. We present two simple instantiations of CTD by using widely adopted acquisition functions in the area. Experimental results show that, across all 446 pairwise comparisons, CTD statistically outperforms state-of-the-art methods in 72.9\% of the cases, performs equivalently in 21.1\%, and is statistically worse in only 6.1\%, with the advantage being particularly evident in settings with very tight evaluation budgets or in high-dimensional problems.
发表机构
- University of Birmingham（伯明翰大学）
机构由 AI 辅助整理，请以论文原文为准。
