Obtain a valid RKHS norm upper bound without prior function-class knowledge

Obtain a valid upper bound on the RKHS norm of the objective function for Gaussian Process Capped Thompson Sampling without prior knowledge of the function class.

Background

GP-CTS removes the $\sqrt{\log N}$ penalty by capping posterior samples with the deterministic envelope $\mu_n(x)+\overline B s_n(x)$, which requires a known valid RKHS norm upper bound $\overline B\geq\|f\|_{\mathcal H_k}$. Although the method achieves minimax rates when such a bound is supplied, obtaining one without prior knowledge of the function class is explicitly identified as an unresolved challenge.