Adapting Nonstationary Multi-output Gaussian Processes to Bayesian Optimization

Multi-objective Bayesian optimization (MOBO) commonly relies on in dependent Gaussian processes with stationary kernels, limiting its ability to represent nonstationary structure and share information between objectives. However, expressive regression models do not necessarily make reliable BO decisions. We study this mismatch for the multi-output low-rank nonstationary (MO-LRN) Gaussian process: 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 provide strong and robust MOBO performance, but realizing this potential requires their structure, calibration, and acquisition optimization to be explicitly adapted to sequential decision making, rather than judged by surrogate accuracy alone.