In Bayesian Optimization (BO) we study black-box function optimization with noisy point evaluations and Bayesian priors. Convergence of BO can be greatly sped up by batching, where multiple evaluations of the black-box function are performed in a single round. The main difficulty in this setting is to propose at the same time diverse and informative batches of evaluation points. In this work, we introduce DPP-Batch Bayesian Optimization (DPP-BBO), a universal framework for inducing batch diversity in sampling based BO by leveraging the repulsive properties of Determinantal Point Processes (DPP) to naturally diversify the batch sampling procedure. We illustrate this framework by formulating DPP-Thompson Sampling (DPP-TS) as a variant of the popular Thompson Sampling (TS) algorithm and introducing a Markov Chain Monte Carlo procedure to sample from it. We then prove novel Bayesian simple regret bounds for both classical batched TS as well as our counterpart DPP-TS, with the latter bound being tighter. Our real-world, as well as synthetic, experiments demonstrate improved performance of DPP-BBO over classical batching methods with Gaussian process and Cox process models.

翻译：在Bayesian Optimination (BO)中,我们研究用噪音点评价和Bayesian 先前的杂音来优化黑箱功能。BO的趋同可以通过批量化来大大加快。BO的趋同,因为对黑箱功能的多次评价是在一回合中进行的。这个环境的主要困难是同时提出多样化的、内容丰富的一批评价点。在这个工作中,我们引入了DPP-Batch Bayesian Optimi化(DPP-BBO),这是一个通用框架,通过利用Ducsminantal Point Procles(DPP)的反性能自然地使批量取样程序多样化,促使BO的批量多样化。我们通过分批量化,通过分批处理,将BOC(DP-TS)的反常性能化,以及合成、实验性能展示DPP-BOB(GOB-B)模型的改进性能。