Competitive multi-task Bayesian optimization with an application in hyperparameter tuning of additive manufacturing

Multi-task Bayesian optimization is an effective approach for optimization involving multiple correlated tasks. Typically, either all the tasks or one primary task should be optimized, depending on the objectives of the problems. We consider optimizing the primary task without explicitly pre-determining which is the primary task. Instead, the primary task is defined as the task whose optimal value is the best among all tasks. Due to the black-box nature of the tasks, the decision makers are not able to identify the primary task beforehand. It is thus critical for the algorithms to recognize and optimize the true primary task. Such problems are called competitive multi-task problems and arise in areas including machine learning and engineering design. In this work, we propose a competitive multi-task Bayesian optimization (CMTBO) algorithm to solve competitive multi-task problems. It selects the query point as well as the task to query in each optimization iteration. We theoretically analyze the regret bounds for the algorithm and test their performances on several synthetic and real-world problems. In addition, our algorithm is applied to a material extrusion (an important technology in additive manufacturing) problem to tune the process parameters and select material types.