Abstract
In material and drug development problems, it is necessary to determine at the lowest possible cost whether the purified material or drug meets the desired quality. When f is an evaluation function of quality and X={x_1, ..., x_n} is a set of features of the material or drug to be evaluated as inputs to f, the above problem can be formulated as a level set estimation problem to classify X into a subset of inputs X_up, where the function value f(x_i) is greater than some threshold value h, and a subset X_low, where f(x_i) is smaller than h. For the level set estimation problem with a single evaluation function, an adaptive decision-making algorithm has been proposed that assumes a Gaussian process model for f and performs efficient classification by sequentially repeating function evaluation according to appropriate measures. On the other hand, in actual problems, it is often required to find conditions that satisfy multiple evaluation indices at the same time, such as "physical property A is below the threshold value h_A, physical property B is above the threshold value h_B, ...". We formulate such a problem as a multi-objective level set estimation problem that finds the common part of the level set of each function when there are two or more evaluation functions, and propose an efficient adaptive decision-making algorithm.
