Bayesian Experimental Design for Finding Reliable Level Set under Input Uncertainty

When the cost of an operational test is expensive, it is desirable to Nagoya Institute of Technology † RIKEN Center for Advanced Intelligence Project ‡ National Institute for Materials Sciences § email:takeuchi.ichiro@nitech.ac.jp be able to identify the region of appropriate input conditions in as few operational tests as possible. If we regard the operational conditions as inputs and the results of the operational tests as outputs of a black-box function, this problem can be viewed as a type of active learning (AL) problem called Level Set Estimation (LSE) . LSE is defined as the problem of identifying the input region in which the outputs of a function are smaller/greater than a certain threshold. In the statistics and machine learning literature, many methods for the LSE problem have been proposed [Bryan et al., 2006, Gotovos et al., 2013, Zanette et al., 2018]. In practical manufacturing applications, since it is often difficult to accurately control the input conditions during the actual usage of the machine, there is a need to guarantee the performance of the machine after properly incorporating the possible variation of input conditions.