Bayesian Optimization with Missing Inputs

Bayesian optimization (BO) is an efficient method for optimizing expensive black-box functions. In real-world applications, BO often faces a major problem of missing values in inputs. The inputs can happen two cases. First, the historical data training contain values. Second, when performing function evaluation (e.g., computing alloy strength heat treatment process), errors may occur thermostat stops working) leading to erroneous situation where computed at random unknown value instead suggested value. To deal with this problem, common approach just simply skips points happen. Clearly, naive cannot utilize efficiently and leads poor performance. paper, we propose novel handle We first find probability distribution each so that impute by drawing sample from its distribution. then develop new acquisition based on well-known Upper Confidence Bound (UCB) function, which considers uncertainty imputed suggesting next point evaluation. conduct comprehensive experiments both synthetic applications show usefulness our method.