R-MBO: A Multi-surrogate Approach for Preference Incorporation in Multi-objective Bayesian Optimisation
This addresses a specific bottleneck in optimization for decision-makers with preferences, but it is incremental as it builds on existing multi-objective Bayesian optimization methods.
The paper tackles the problem of incorporating decision-maker preferences into multi-objective Bayesian optimization by proposing a multi-surrogate approach that overcomes limitations of existing mono-surrogate methods, showing improved performance on benchmark and real-world problems.
Many real-world multi-objective optimisation problems rely on computationally expensive function evaluations. Multi-objective Bayesian optimisation (BO) can be used to alleviate the computation time to find an approximated set of Pareto optimal solutions. In many real-world problems, a decision-maker has some preferences on the objective functions. One approach to incorporate the preferences in multi-objective BO is to use a scalarising function and build a single surrogate model (mono-surrogate approach) on it. This approach has two major limitations. Firstly, the fitness landscape of the scalarising function and the objective functions may not be similar. Secondly, the approach assumes that the scalarising function distribution is Gaussian, and thus a closed-form expression of an acquisition function e.g., expected improvement can be used. We overcome these limitations by building independent surrogate models (multi-surrogate approach) on each objective function and show that the distribution of the scalarising function is not Gaussian. We approximate the distribution using Generalised value distribution. We present an a-priori multi-surrogate approach to incorporate the desirable objective function values (or reference point) as the preferences of a decision-maker in multi-objective BO. The results and comparison with the existing mono-surrogate approach on benchmark and real-world optimisation problems show the potential of the proposed approach.