arXiv:2605.00237cs.LGstat.ML2026-05

用分块方法让贝叶斯优化速度翻倍,还更准。

Bayesian Optimization in Linear Time

论文配图:Bayesian Optimization in Linear Time
图 1 · 摘自论文原文
  • 用递归二分法切分搜索空间,替代全局建模。
  • 在6到124维测试函数上表现优于主流库,且时间线性增长。
  • 适合高维、计算代价大的优化任务,如超参调优。

贝叶斯优化是一种用于最小化昂贵评估目标函数的序列方法,通过使用所有收集数据训练高斯过程模型,并自适应地结合全局探索与局部利用,在机器学习、汽车工程和强化学习等领域广泛应用。然而,标准方法存在两个问题:1)训练集规模下计算复杂度为立方级,最终变得不可行;2)全局建模未必最优,因最小化具有局部性。本文采用灵活且递归的二分法划分搜索空间,改进了标准贝叶斯优化的建模与选择策略,使二者协同工作。在7个挑战性测试函数上(维度从6到124),我们的方法性能全面优于常用贝叶斯优化库,且计算复杂度为线性。

原文摘要 · Abstract (English)

Bayesian optimization is a sequential method for minimizing objective functions that are expensive to evaluate and about which few assumptions can be made. By using all gathered data to train a Gaussian process model for the function and adaptively employing a mixture of global exploration and local exploitation, this method has been used for optimization in many fields including machine learning, automotive engineering and reinforcement learning. However, the standard method suffers from two problems: 1) with cubic computational complexity in the training-set size it eventually becomes computationally infeasible to train the model, and 2) globally modeling the objective function is not necessarily optimal given the local nature of minimization. Using flexible and recursive binary partitioning of the search space, we adapt both the modeling and acquisitive aspects of standard Bayesian optimization to work harmoniously with the partitioning scheme, thereby ameliorating both standard shortcomings. We compare our method against a commonly used Bayesian optimization library on seven challenging test functions, ranging in dimensionality from $6$ to $124$, and show that our method achieves superior optimization performance in all tests. In addition our method has linear computational complexity.

贝叶斯优化高维优化线性复杂度加速算法

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