Machine Learning Algorithms for Improving Black Box Optimization Solvers

Abstract

Black-box optimization (BBO) addresses problems where objectives are accessible only through costly queries without gradients or explicit structure. Classical derivative-free methods---line search, direct search, and model-based solvers such as Bayesian optimization---form the backbone of BBO, yet often struggle in high-dimensional, noisy, or mixed-integer settings. Recent advances use machine learning (ML) and reinforcement learning (RL) to enhance BBO: ML provides expressive surrogates, adaptive updates, meta-learning-based algorithm selection, and generative models, while the RL--BBO interface includes dynamic operator configuration, robust policy search, and meta-optimization across tasks. This paper surveys these developments, covering representative algorithms such as the modular model-based optimization framework (mlrMBO), zeroth-order adaptive momentum methods (ZO-AdaMM), automated BBO (ABBO), distributed block-wise optimization (DiBB), partition-based Bayesian optimization (SPBOpt), the transformer-based optimizer (B2Opt), diffusion-model-based BBO, surrogate-assisted RL for differential evolution (Surr-RLDE), robust BBO (RBO), coordinate-ascent MORE with step size adaptation (CAS-MORE), log-barrier stochastic gradient descent (LB-SGD), policy improvement with black-box (PIBB), and offline Q-learning with Mamba backbones (Q-Mamba). We further review benchmark efforts such as the NeurIPS 2020 BBO Challenge and the MetaBox framework. A controlled numerical study further confirms that ML-based candidate screening can improve the evaluation-budget performance of direct search and differential evolution, while the benefit remains solver-dependent.