Hypervolume-based Multi-objective Bayesian Optimization with Student-t Processes
This work addresses optimization problems with multiple conflicting objectives, offering a novel method for researchers and practitioners in fields like engineering or machine learning, but it appears incremental as it adapts an existing framework with a different prior.
The authors tackled the challenge of multi-objective Bayesian optimization by developing an analytical expression for hypervolume-based probability of improvement using Student-t processes, showing effectiveness on a difficult problem where traditional Gaussian processes struggle.
Student-$t$ processes have recently been proposed as an appealing alternative non-parameteric function prior. They feature enhanced flexibility and predictive variance. In this work the use of Student-$t$ processes are explored for multi-objective Bayesian optimization. In particular, an analytical expression for the hypervolume-based probability of improvement is developed for independent Student-$t$ process priors of the objectives. Its effectiveness is shown on a multi-objective optimization problem which is known to be difficult with traditional Gaussian processes.