Pareto-frontier Entropy Search with Variational Lower Bound Maximization
This work addresses a bottleneck in multi-objective optimization for researchers and practitioners, though it is incremental as it builds on existing Bayesian optimization frameworks.
The study tackled the challenge of approximating the information gain in multi-objective Bayesian optimization when the complete Pareto-frontier is unknown, by proposing a mixture distribution method with variational lower bound optimization, which showed effectiveness in scenarios with many objective functions.
This study considers multi-objective Bayesian optimization (MOBO) through the information gain of the Pareto-frontier. To calculate the information gain, a predictive distribution conditioned on the Pareto-frontier plays a key role, which is defined as a distribution truncated by the Pareto-frontier. However, it is usually impossible to obtain the entire Pareto-frontier in a continuous domain, and therefore, the complete truncation cannot be known. We consider an approximation of the truncate distribution by using a mixture distribution consisting of two possible approximate truncation obtainable from a subset of the Pareto-frontier, which we call over- and under-truncation. Since the optimal balance of the mixture is unknown beforehand, we propose optimizing the balancing coefficient through the variational lower bound maximization framework, by which the approximation error of the information gain can be minimized. Our empirical evaluation demonstrates the effectiveness of the proposed method particularly when the number of objective functions is large.