Neural Evolution Strategy for Black-box Pareto Set Learning
Chengyu Lu, Zhenhua Li, Xi Lin, Ji Cheng, Qingfu Zhang
Multi-objective optimization problems (MOPs), which involve optimizing multiple conflicting objectives simultaneously, are common in many real-world applications. Recently, Pareto Set Learning (PSL) has emerged as a powerful paradigm for solving MOPs, enabling the on-demand generation of tailored Pareto optimal solutions without requiring repeated optimization. However, applying PSL to black-box objectives, particularly those exhibiting non-separability, high dimensionality, or other complex properties, remains poorly understood. To bridge this gap, we propose leveraging evolution strategies (ESs), a class of specialized black-box optimization algorithms, within the PSL paradigm. Traditional ESs capture the complex dimensional dependencies of problems less efficiently, which can significantly hinder their performance in PSL. To tackle this issue, we suggest encapsulating the dependencies within a neural network, which is then trained using a novel gradient estimation method. The proposed method, termed Neural-ES, is evaluated using a bespoke benchmark suite for black-box PSL. Experimental comparisons with other methods demonstrate the efficiency of Neural-ES, underscoring its suitability for learning the Pareto sets of challenging black-box MOPs.