Bridging Spherical Black-Box Optimizers

Modern engineering workflows increasingly rely on massive parallel simulation, driving the need for scalable, large-batch Bayesian Optimization (BO). Existing batch BO methods, however, incur large computational cost or rely on approximations that erode batch diversity. We propose B3O (Boltzmann Batch Bayesian Optimization), a framework that reframes batch generation as a pure sampling problem: drawing samples directly from the Boltzmann distribution defined by the acquisition function avoids the bottlenecks of existing large-batch methods. Theoretically, we prove that queries sampled from this distribution incur only negligible additional regret. Empirically, B3O outperforms existing batch BO methods on standard synthetic benchmarks and adapts robustly across complex applied tasks, including multi-objective electrode design and mixed-variable race car configuration.

Multi-objective Bayesian optimization (MOBO) provides a principled framework for optimizing multiple expensive black-box functions. However, existing MOBO methods often struggle with coverage, scalability, and handling constraints and preferences. In this work we propose STAGE-BO, Sequential Targeting Adaptive Gap-Filling $\varepsilon$-Constraint Bayesian Optimization: by analyzing the coverage of the surrogate Pareto front, our method identifies the Pareto front point with the largest uncovered gap, and uses its coordinates to define adaptive constraints in $\varepsilon$-constraint method, which transforms the problem into a sequence of inequality-constrained subproblems, efficiently solved via constrained expected improvement acquisition. Our approach provides uniform Pareto coverage without hypervolume computation and naturally handles constraints and preferences. Experiments on synthetic and real-world benchmarks demonstrate superior coverage and competitive hypervolume performance against state-of-the-art baselines. Our code implementation can be found at https://github.com/YangYaohong1/STAGE-BO.

Expensive black-box optimization is ubiquitous in science and engineering, where function evaluations are costly and the evaluation budget is limited. Traditional evolutionary algorithms and Meta-BlackBox Optimization (MetaBBO) approaches typically consume most evaluations on candidate selection, often wasting precious budget on inferior solutions. Although surrogate-assisted evolution and Bayesian optimization aim to reduce evaluations through surrogate models, constructing an accurate global model from limited data remains challenging, and model bias can easily trap the search in local optima. To overcome these limitations, we propose NeurGO, a generative MetaBBO framework that directly synthesizes elite candidates from historical population states. Specifically, we employ an attention-based encoder to capture the population-level search trend and condition a decoder on this representation to generate high-quality candidates, avoiding the expensive evaluation of large offspring pools. We then design a quality-diversity loss to maintain solution quality and population diversity throughout the search. Through extensive benchmarking on CEC 2008 and the COCO BBOB test suites, our method achieves better optimization performance under the same evaluation budget and exhibits faster convergence.