In modern pharmaceutical studies, researchers have found that both the doses and timing of administration of drug components in combinatorial drugs have significant impact on treatment efficacy. However, these studies often have constraints, such as the minimum separation time and maximum number of drug components. To find the best drug combinations, simultaneous optimization for both the doses and timing of administration is required, where one-shot experimental designs are often inefficient. In this work, we propose a novel active learning procedure along with a new Gaussian process model to efficiently identify the optimal configurations within only a few experimental trials. The superiority of the proposed method is illustrated via different simulation studies and real case study.
