A Simple and Efficient Approach to Batch Bayesian Optimization

TL;DR

This paper addresses the inefficient scaling of batch Bayesian optimization when large batch sizes are used. It introduces Expected SubSpace Improvement (ESSI), a simple acquisition criterion that selects one point from each of multiple axis-aligned subspaces, enabling parallel evaluation and reducing optimization difficulty by effectively lowering the acquisition dimensionality. The authors provide a complete computational framework, including random subspace selection and parallel ESSI optimization, and demonstrate through extensive experiments on the CEC2017 suite that ESSI achieves substantial wall-clock speedups and competitive or superior final regrets compared to seven state-of-the-art batch EI methods, across $d=10$ and $d=30$ and batch sizes up to $q=128$. The approach is noted as simple, parameter-free, and easily implementable, with a GitHub Matlab implementation available, and future work suggested for extending to constrained optimization. Overall, ESSI offers a practical and scalable route to accelerate batch Bayesian optimization in parallel computing environments while maintaining strong optimization performance.

Abstract

Extending Bayesian optimization to batch evaluation can enable the designer to make the most use of parallel computing technology. However, most of current batch approaches do not scale well with the batch size. That is, their performances deteriorate dramatically as the batch size increases. To address this issue, we propose a simple and efficient approach to extend Bayesian optimization to large-scale batch evaluation in this work. Different from existing batch approaches, the idea of the new approach is to draw a batch of axis-aligned subspaces of the original problem and select one acquisition point from each subspace. To achieve this, we propose the expected subspace improvement criterion to measure the amount of the improvement that a candidate point can achieve within a certain axis-aligned subspace. By optimizing these expected subspace improvement functions simultaneously, we can get a batch of query points for parallel evaluation. Numerical experiments show that our proposed approach can speedup the convergence significantly when compared with the sequential Bayesian optimization algorithm, and performs very competitively when compared with seven batch Bayesian optimization algorithms. A Matlab implementation of the proposed approach is available at https://github.com/zhandawei/Expected_Subspace_Improvement_Batch_Bayesian_Optimization.

Figures (8)

• Figure 1: Gaussian process approximation and the corresponding expected improvement of $f(x) = x\sin(x)$.
• Figure 2: Six ESSI functions of a 3-dimensional problem.
• Figure 3: Acquisition optimization results on a 3-dimensional problem.
• Figure 4: Convergence curves of the sequential EI and the proposed ESSI on 10-D and 30-D problems.
• Figure 5: Acquisition optimization time of the proposed ESSI and the EI functions.