Multi-objective Bayesian optimisation with preferences over objectives
This work addresses the challenge of efficiently exploring Pareto fronts with preferences in optimization, which is incremental as it builds on existing Bayesian optimization methods.
The paper tackles the problem of multi-objective Bayesian optimization by incorporating user-defined preference-order constraints on objectives, resulting in an algorithm that selects Pareto-optimal points satisfying these constraints and demonstrates performance on synthetic and real-world problems.
We present a multi-objective Bayesian optimisation algorithm that allows the user to express preference-order constraints on the objectives of the type "objective A is more important than objective B". These preferences are defined based on the stability of the obtained solutions with respect to preferred objective functions. Rather than attempting to find a representative subset of the complete Pareto front, our algorithm selects those Pareto-optimal points that satisfy these constraints. We formulate a new acquisition function based on expected improvement in dominated hypervolume (EHI) to ensure that the subset of Pareto front satisfying the constraints is thoroughly explored. The hypervolume calculation is weighted by the probability of a point satisfying the constraints from a gradient Gaussian Process model. We demonstrate our algorithm on both synthetic and real-world problems.