Learning What to Evaluate: Correlation-Aware Decoupling for Multiobjective Bayesian Optimization

Multi-objective Bayesian optimization (MOBO) commonly relies on independent Gaussian processes (GPs) with stationary kernels, limiting its ability to represent nonstationary structure and share information between objectives. However, expressive nonstationary GPs do not necessarily make reliable BO decisions. We study this mismatch for the multi-output low-rank nonstationary (MO-LRN) GP: strong training fit can coexist with large off-design errors and optimistic acquisition predictions. We introduce MOLRN-BO, which combines a regularized shared-spectral surrogate with objective-specific residuals, prequential mean correction and tempered covariance scaling, and Pareto-local qLogEHVI optimization with periodic global search. Experiments on 12 deterministic bi-objective benchmarks show that MOLRN-BO substantially improves upon the original MO-LRN and achieves the best average problem ranks for final normalized hypervolume and normalized inverted generational distance among nine evaluated algorithms. It also achieves the strongest adverse-tail performance while remaining competitive with the leading baselines in anytime optimization. Ablation studies further show that the shared spectral construction improves off-design prediction, the local--global decision policy improves optimization performance, and hierarchical calibration reduces systematic candidate bias. These results demonstrate that nonstationary multi-output surrogates can deliver strong and robust MOBO performance when their structure and use are explicitly adapted to the demands of sequential optimization.

Multi-objective Bayesian optimization (MOBO) provides a principled framework for optimizing multiple expensive black-box functions. However, existing MOBO methods often struggle with coverage, scalability, and handling constraints and preferences. In this work we propose STAGE-BO, Sequential Targeting Adaptive Gap-Filling $\varepsilon$-Constraint Bayesian Optimization: by analyzing the coverage of the surrogate Pareto front, our method identifies the Pareto front point with the largest uncovered gap, and uses its coordinates to define adaptive constraints in $\varepsilon$-constraint method, which transforms the problem into a sequence of inequality-constrained subproblems, efficiently solved via constrained expected improvement acquisition. Our approach provides uniform Pareto coverage without hypervolume computation and naturally handles constraints and preferences. Experiments on synthetic and real-world benchmarks demonstrate superior coverage and competitive hypervolume performance against state-of-the-art baselines. Our code implementation can be found at https://github.com/YangYaohong1/STAGE-BO.

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 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.