Exact Worst-Case Frontiers for Multivariate and Pearson Priming

Determine the tight worst-case regret rates as functions of horizon and dimension for powered multivariate and Pearson feature priming, thereby closing the gap between the established rank upper bound and the available lower bounds.

Background

The paper proves the exact worst-case order $\Theta_\alpha(\min\{T,d\})$ for powered univariate priming. For multivariate and Pearson priming, it establishes lower bounds of order $\Omega(\min\{T,\sqrt d\})$ in the relevant constructions and a general rank-based upper bound of order $O(\min\{T,d\})$.

Consequently, the precise dependence on dimension and horizon for the multivariate and Pearson rules is unresolved. The same issue is reiterated in the conclusion as the absence of matching frontiers.