Pareto Set Learning (PSL) is a promising approach for approximating the entire Pareto front in multi-objective optimization (MOO) problems. However, existing derivative-free PSL methods are often unstable and inefficient, especially for expensive black-box MOO problems where objective function evaluations are costly. In this work, we propose to address the instability and inefficiency of existing PSL methods with a novel controllable PSL method, called Co-PSL. Particularly, Co-PSL consists of two stages: (1) warm-starting Bayesian optimization to obtain quality Gaussian Processes priors and (2) controllable Pareto set learning to accurately acquire a parametric mapping from preferences to the corresponding Pareto solutions. The former is to help stabilize the PSL process and reduce the number of expensive function evaluations. The latter is to support real-time trade-off control between conflicting objectives. Performances across synthesis and real-world MOO problems showcase the effectiveness of our Co-PSL for expensive multi-objective optimization tasks.

翻译：Pareto集学习（PSL）是近似多目标优化（MOO）问题中完整Pareto前沿的一种有前景方法。然而，现有无导数PSL方法往往不稳定且效率低下，尤其是在目标函数评估成本高昂的昂贵黑箱MOO问题中。本研究提出一种名为Co-PSL的新型可控PSL方法，以解决现有PSL方法的不稳定性和低效性问题。具体而言，Co-PSL包含两个阶段：（1）暖启动贝叶斯优化，用于获取高质量高斯过程先验；（2）可控Pareto集学习，用于精确获取从偏好到对应Pareto解的参数化映射。前者有助于稳定PSL过程并减少昂贵函数评估次数，后者则支持对冲突目标进行实时权衡控制。在合成与真实MOO问题中的性能表现验证了Co-PSL在昂贵多目标优化任务中的有效性。