Supplementary Material Misspecified GP Bandit Optimization Ilija Bogunovic and Andreas Krause (NeurIPS 2021) A GP bandits: Useful definitions and auxiliary results (Realizable setting)

Such assumptions on the noise variables are frequently used in bandit optimization. Gaussian process with posterior mean and variance that correspond to Eq. (8) and Eq. It also allows us to rewrite Eq. Gaussian Process (supported on D) with the corresponding kernel function. Suppose the learner's hypothesis class is While the first two terms in this bound can be effectively controlled and bounded as in the proof of Theorem 1, the last term, i.e., Such a function can easily be constructed, e.g., via the approach outlined in [36].