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 sensor design 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中一项关键但充满挑战的任务。这一挑战源于需要大量的试错过程，通常通过模拟或实地实验进行。幸运的是，序贯最优设计（在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。边缘设备连接性的增强为贝叶斯优化提出了一种新的协作范式。在这种范式中，不同客户端通过有效分配实验工作来相互借鉴优势，从而改进并加速其最优设计过程。为此，我们将共识概念引入贝叶斯优化，即客户端就下一步采样的设计达成一致（即达成共识）。我们的方法提供了一个通用且灵活的框架，能够整合不同的协作机制。基于此，我们提出了过渡性协作机制，其中客户端在初期阶段更多地依赖彼此，以在数据稀缺时应对早期阶段，而在后期阶段则专注于各自的目标，以获得客户端特定的解决方案。理论上，我们证明了所提框架的遗憾值呈次线性增长。通过模拟数据集和一项现实世界的协作传感器设计实验，我们在实证中表明，该框架能够有效加速并改进最优设计过程，并使所有参与者受益。