Training of Deep Generative Models Using Several Loss Functions and its Application to Constrained Black-Box Optimization

Abstract

In constrained black-box optimization, optimizing the objective function is extremely difficult if the feasible domain X is a set of discrete feasible regions and even obtaining a feasible solution is difficult. This paper proposes a technique to transform the search space S into a simple one with almost no constraints. In detail, we create a map from the input space Z to X, Decoder G: Z -> X, and use Z of G as the search space to achieve the above transformation. To perform mapping to discrete regions, we make Decoder G concatenated small neural network models (NNs) with a shortcut connection, and we define loss functions for each NN. This prevents mode collapse, which is a well-known problem in deep generative models. In the experiments, we demonstrate the usefulness of the proposed technique using a test problem where the volume ratio of X to S is less than 1e-7.