Minimax-Optimal Small-Loss Bounds for Online Linear Optimisation on ${\ell }_p$ Balls

Jack J. Mayo

We study full-information online linear optimisation on the unit ${\ell }_p$ ball in ${\mathbb{R}}^d$, for fixed $2\le p<\infty$ and losses of dual norm at most one. Let ${\Delta }_T$ denote th…