arXiv:2601.22131cs.LG2026-01

用元学习加速多目标优化,提升数据效率。

SMOG: Scalable Meta-Learning for Multi-Objective Bayesian Optimization

  • 基于多输出高斯过程构建结构化先验,显式建模目标间相关性。
  • 支持层级并行训练,可线性扩展至大量元任务,提升效率。
  • 适用于有历史数据的多目标优化场景,尤其适合评估昂贵的问题。

多目标优化旨在解决存在冲突目标的问题,但其评估通常耗时或成本高昂,限制了可用评估预算。在许多应用中,可通过元学习利用相关优化任务的历史数据以加速求解。贝叶斯优化作为处理高成本黑箱问题的有力方法,已被分别拓展至元学习和多目标优化领域,但同时兼顾两者的方案仍较少。本文提出SMOG——一种基于多输出高斯过程的可扩展、模块化元学习模型,显式学习目标间的相关性。SMOG在元任务与目标任务之间构建结构化的联合高斯过程先验,经元数据条件化后,得到目标任务的闭式先验,以合理方式将元数据不确定性传播至目标代理模型。该方法支持层级化、并行训练,实现与元任务数量的线性扩展。生成的代理模型可无缝集成标准多目标贝叶斯优化采集函数。实验表明,该方法在代表性基准和应用中始终表现优异,展现出强数据效率。

原文摘要 · Abstract (English)

Multi-objective optimization aims to solve problems with competing objectives. Evaluating such problems is often slow or expensive, limiting the budget of evaluations. In many applications, historical data from related optimization tasks is available and can be leveraged via meta-learning to accelerate optimization. Bayesian optimization, as a promising technique for expensive black-box problems, has been extended independently to meta-learning and multi-objective optimization, but methods that simultaneously address both settings remain largely unexplored. We propose SMOG-a scalable and modular meta-learning model based on a multi-output Gaussian process-that explicitly learns correlations between objectives. SMOG builds a structured joint Gaussian process prior across meta- and target tasks and, after conditioning on metadata, yields a closed-form prior for the target task. This construction propagates metadata uncertainty into the target surrogate in a principled way. SMOG supports hierarchical, parallel training, achieving linear scaling with the number of meta-tasks. The resulting surrogate integrates seamlessly with standard multi-objective Bayesian optimization acquisition functions. We demonstrate that our method is consistently competitive, delivering strong data efficiency across representative benchmarks and applications.

元学习多目标优化贝叶斯优化高斯过程

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