 $${\mathbb{P}\,}\left[ C \inf_{{\boldsymbol{\theta}}\in \Theta_N}  h^0(s,f_{{\boldsymbol{\theta}}}) \geq h^0(s, {\mathscr{F}}) +  \frac{D_{{\mathscr{F}}}}{n} +  \xi \right] \leq e^{- n \xi}$$ where $C > 0$ depends only on $\kappa, \