Multi objective optimisation improves by separating learning steps
Converge Then Diversify: Decoupling Convergence and Diversity in Multi-Objective Bayesian Optimisation
Artificial Intelligence
Summary
Optimizing things with multiple goals usually means finding a set of best options that are both close to the ideal and diverse across choices. The authors show that doing these two steps at once can be hard when you have little time or resources. They suggest first focusing on finding a single good solution, then spreading out to cover many solutions later. Their tests show this two-step way works better than existing methods, especially when resources are tight or problems are complex.
What this means in practice
- •For machine learning engineers: Optimize models with multiple conflicting objectives efficiently when evaluation budgets are very tight.
- •For design optimization teams: Improve multi-objective product design by first finding a good solution before exploring diverse trade-offs to save costly evaluations.
Authors
Chao Jiang, Yueling Huang, Miqing Li
Abstract
Multi-objective Bayesian optimisation (MOBO) is a sample-efficient approach for optimising expensive black-box functions with multiple objectives. In MOBO, the goal is to adequately approximate the Pareto front; that is, to obtain a high-quality solution set with 1) good convergence (closeness to the Pareto front) and 2) good diversity (spread across the Pareto front). Existing MOBO methods typically aim to accomplish these two tasks simultaneously, i.e., driving the search towards the Pareto front while maintaining a diverse set of nondominated solutions, such that the solutions, ideally, can gradually approach the entire front. When sufficient search budgets are available, this approach is effective. However, considering both convergence and diversity throughout the search is not easy and requires careful design. Under very tight budgets, there may not be enough solutions generated to be able to simultaneously approach the entire Pareto front. To address this issue, this paper proposes a \textit{converge-then-diversify} (CTD) approach that decouples convergence and diversity into two stages. In the first stage, CTD focuses on convergence, aiming to quickly drive the search toward a single point on the Pareto front. In the second stage, CTD focuses on diversity, aiming to spread solutions across the front. We present two simple instantiations of CTD by using widely adopted acquisition functions in the area. Experimental results show that, across all 446 pairwise comparisons, CTD statistically outperforms state-of-the-art methods in 72.9\% of the cases, performs equivalently in 21.1\%, and is statistically worse in only 6.1\%, with the advantage being particularly evident in settings with very tight evaluation budgets or in high-dimensional problems.