Bilevel Optimization by Conditional Bayesian Optimization

Bilevel optimization problems have two decision-makers: a leader and a follower (sometimes more than one of either, or both). The leader must solve a constrained optimization problem in which some decisions are made by the follower. These problems are much harder to solve than those with a single decision-maker, and efficient optimal algorithms are known only for special cases. A recent heuristic approach is to treat the leader as an expensive black-box function, to be estimated by Bayesian optimization. We propose a novel approach called ConBaBo to solve bilevel problems, using a new conditional Bayesian optimization algorithm to condition previous decisions in the bilevel decision-making process. This allows it to extract knowledge from earlier decisions by both the leader and follower. We present empirical results showing that this enhances search performance and that ConBaBo outperforms some top-performing algorithms in the literature on two commonly used benchmark datasets.