Surrogate Learning in Meta-Black-Box Optimization: A Preliminary Study

Abstract: Recent Meta-Black-Box Optimization (MetaBBO) approaches have shown possibility of enhancing the optimization performance through learning meta-level policies to dynamically configure low-level optimizers. However, existing MetaBBO approaches potentially consume massive function evaluations to train their meta-level policies. Inspired by the recent trend of using surrogate models for cost-friendly evaluation of expensive optimization problems, in this paper, we propose a novel MetaBBO framework which combines surrogate learning process and reinforcement learning-aided Differential Evolution algorithm, namely Surr-RLDE, to address the intensive function evaluation in MetaBBO. Surr-RLDE comprises two learning stages: surrogate learning and policy learning. In surrogate learning, we train a Kolmogorov-Arnold Networks (KAN) with a novel relative-order-aware loss to accurately approximate the objective functions of the problem instances used for subsequent policy learning. In policy learning, we employ reinforcement learning (RL) to dynamically configure the mutation operator in DE. The learned surrogate model is integrated into the training of the RL-based policy to substitute for the original objective function, which effectively reduces consumed evaluations during policy learning. Extensive benchmark results demonstrate that Surr-RLDE not only shows competitive performance to recent baselines, but also shows compelling generalization for higher-dimensional problems. Further ablation studies underscore the effectiveness of each technical components in Surr-RLDE. We open-source Surr-RLDE at https://github.com/GMC-DRL/Surr-RLDE.