Regret guarantees under candidate-set misspecification

Derive regret guarantees for HE-CV-UCB that degrade quantitatively with the misspecification of the best candidate surrogate, rather than requiring the candidate set to contain a correctly specified Gaussian-process model.

Background

The theoretical analysis of HE-CV-UCB assumes that the finite candidate set contains at least one correctly specified Gaussian-process surrogate whose reproducing-kernel Hilbert-space confidence bounds contain the unknown objective. In the real-world transfer experiments, however, the transferred candidate pool is not guaranteed to contain such a model, although the algorithm can still perform effectively in practice.

The unresolved problem is to extend the regret theory to this misspecified setting by relating performance to the quality of the best available candidate, in analogy with misspecification-dependent guarantees for expectation-based Bayesian optimization. Such a result would make the theory applicable when every transferred surrogate is imperfect.

References

Our theoretical guarantee assumes that a correctly specified surrogate is contained in the candidate set. The real-world experiments suggest that HE-CV-UCB remains effective beyond this setting, but deriving regret guarantees that degrade with the misspecification of the best candidate, in the spirit of \citet{bogunovic-neurips21a}, remains an open direction.

— Bayesian Optimization of CVaR with Unknown Hyperparameters  (2610.18306 - Margraf et al., 13 Oct 2026) in Section 6, paragraph “Limitations and future work”