aiqbench analysis
This research introduces a two-stage "converge-then-diversify" strategy for multi-objective Bayesian optimization, decoupling the simultaneous pursuit of solution quality and distribution. By prioritizing convergence first before expanding diversity, the method significantly outperforms existing approaches in scenarios with tight evaluation budgets or high-dimensional problems. The findings offer a practical framework for improving sample efficiency in expensive black-box function optimization tasks.
Converge Then Diversify: Decoupling Convergence and Diversity in Multi-Objective Bayesian Optimisation
arXiv:2609.13396v1 Announce Type: new 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.
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.
Artificial Intelligence (cs.AI); Machine Learning (stat.ML)
arXiv:2609.13396 [cs.AI]
(or arXiv:2609.13396v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2609.13396 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 354 words
Related coverage
Learning Pareto Stationary Fronts via Single-Pass Backpropagation
arXiv · Oct 6, 2026
Multi-Agent Flow Matching with Decoupled Generative Guidance
arXiv · Sep 30, 2026
Game-Theoretic Disempowerment: Loss of Control to Agencyless AI
LessWrong · Sep 27, 2026
Diversity-Driven Offline Multi-Objective Optimization via Nested Pareto Set Learning
arXiv · Jun 16, 2026