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In many scientific and engineering applications, Bayesian Optimization (BO) is a powerful tool for hyperparameter tuning of a machine learning model, materials design and discovery, etc. Multi-task BO is a general method to efficiently optimize multiple different, but correlated, “black-box” functions. The objective of this work is to develop an algorithm for multi-task BO with automatic task selection so that only one task evaluation is needed per query round. Specifically, a new algorithm, namely, Multi-Task Gaussian Process Upper Confidence Bound (MT-GPUCB), is proposed to achieve this objective. The MT-GPUCB is a two-step algorithm, where the first step chooses which query point to evaluate, and the second step automatically selects the most informative task to evaluate. Under the bandit setting, a theoretical analysis is provided to show that our proposed MT-GPUCB is  no-regret  under some mild conditions. Our proposed algorithm is verified experimentally on a range of synthetic functions. In addition, our algorithm is applied to Additive Manufacturing simulation software, namely, Flow-3D Weld, to determine material property values, ensuring the quality of simulation output. The results clearly show the advantages of our query strategy for both design point and task.

Multi-task Gaussian process upper confidence bound for hyperparameter tuning and its application for simulation studies of additive manufacturing