Optimal design is a critical yet challenging task within many applications. This challenge arises from the need for extensive trial and error, often done through simulations or running field experiments. Fortunately, sequential optimal design, also referred to as Bayesian optimization when using surrogates with a Bayesian flavor, has played a key role in accelerating the design process through efficient sequential sampling strategies. However, a key opportunity exists nowadays. The increased connectivity of edge devices sets forth a new collaborative paradigm for Bayesian optimization. A paradigm whereby different clients collaboratively borrow strength from each other by effectively distributing their experimentation efforts to improve and fast-track their optimal design process. To this end, we bring the notion of consensus to Bayesian optimization, where clients agree (i.e., reach a consensus) on their next-to-sample designs. Our approach provides a generic and flexible framework that can incorporate different collaboration mechanisms. In lieu of this, we propose transitional collaborative mechanisms where clients initially rely more on each other to maneuver through the early stages with scant data, then, at the late stages, focus on their own objectives to get client-specific solutions. Theoretically, we show the sub-linear growth in regret for our proposed framework. Empirically, through simulated datasets and a real-world collaborative material discovery experiment, we show that our framework can effectively accelerate and improve the optimal design process and benefit all participants.

翻译：最优设计是许多应用场景中至关重要但又充满挑战的任务。这一挑战源于需要大量的试错过程，通常通过仿真或实地实验来完成。幸运的是，序贯最优设计（当使用具有贝叶斯风格的代理模型时也称为贝叶斯优化）通过高效的序贯采样策略在加速设计过程中发挥了关键作用。然而，当前存在一个重要机遇：边缘设备互联性的增强为贝叶斯优化提出了一种新的协作范式。在该范式下，不同客户通过有效分配其试验工作来相互借力，从而加速并优化各自的最优设计进程。为此，我们将共识概念引入贝叶斯优化，使客户能够就下一步待采样的设计方案达成一致（即形成共识）。本文提出的通用灵活框架可整合多种协作机制。在此基础上，我们提出了过渡性协作机制：在早期数据匮乏阶段，客户主要依赖彼此协作来推进进程；而在后期阶段，则聚焦自身目标以获取定制化解决方案。理论上，我们证明了所提出框架的遗憾值呈次线性增长。通过仿真数据集与真实世界的协作材料发现实验，实证表明该框架能有效加速并优化最优设计进程，使所有参与者受益。