Impact of evaluation noise in the context of multi-objective Bayesian optimization with the intrinsic coregionalization model

Multi-objective Bayesian optimization (MOBO) is a powerful framework for optimizing black-box functions with conflicting objectives and costly evaluations. A key component in MOBO is the probabilistic surrogate model used to guide the search for the optimum. A simple approach is to use independent Gaussian processes (GPs), one per objective. A more powerful method is to use multi-output GPs, such as those based on the intrinsic coregionalization model (ICM), to exploit correlations between objectives. However, with this model, often independent observation noise across objectives is assumed, which ignores part of the correlation structure. In this work, we isolate and analyze the role of observational noise in MOBO with ICM-based multi-output GPs. We consider models that can capture correlations in the observational noise, and study how the presence and structure of noise affect the joint predictive distribution, the considered acquisition function, and ultimately the optimization performance.Through theoretical analysis and extensive synthetic and real-world experiments, we show that multi-output GPs can significantly improve optimization efficiency when the evaluations are noisy. Importantly, however, when the evaluations are noiseless, we observe, both theoretically and empirically, only small gains by considering multi-output GPs, and cheaper independent GPs may be preferred. Furthermore, our synthetic experiments show that explicitly modeling noise correlations provides additional advantages when the objectives themselves are negatively correlated. In real-world problems, however, we have observed mixed results regarding modeling noise correlations. There are small gains in an ensemble benchmark and clearer gains, similar to those observed in the synthetic experiments, in a neural-network benchmark. These findings provide practical insights into when and how to use ICMs for MOBO.