Batch Bayesian optimisation and Bayesian quadrature have been shown to be sample-efficient methods of performing optimisation and quadrature where expensive-to-evaluate objective functions can be queried in parallel. However, current methods do not scale to large batch sizes -- a frequent desideratum in practice (e.g. drug discovery or simulation-based inference). We present a novel algorithm, SOBER, which permits scalable and diversified batch global optimisation and quadrature with arbitrary acquisition functions and kernels over discrete and mixed spaces. The key to our approach is to reformulate batch selection for global optimisation as a quadrature problem, which relaxes acquisition function maximisation (non-convex) to kernel recombination (convex). Bridging global optimisation and quadrature can efficiently solve both tasks by balancing the merits of exploitative Bayesian optimisation and explorative Bayesian quadrature. We show that SOBER outperforms 11 competitive baselines on 12 synthetic and diverse real-world tasks.

翻译：摘要：批量贝叶斯优化与贝叶斯求积已被证明是高效的采样方法，适用于需要并行查询昂贵评估目标函数的优化与求积任务。然而，现有方法无法扩展到大批量规模——这却是实践中常见的需求（如药物发现或基于模拟的推理）。我们提出了一种新型算法SOBER，该算法在离散与混合空间中，支持任意采集函数和核函数的可扩展且多样化的批量全局优化与求积。该方法的核心创新在于将全局优化的批量选择问题重新表述为求积问题，从而将采集函数最大化（非凸问题）松弛为核重组（凸问题）。通过平衡开发性贝叶斯优化与探索性贝叶斯求积的各自优势，全局优化与求积的融合能够高效解决这两类任务。实验表明，SOBER在12项合成任务和多样化真实世界任务中超越了11个竞争基线方法。