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Minimax-Optimal Small-Loss Bounds for Online Linear Optimisation on $\ell_p$ Balls
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 $Δ_T$ denote the cumulative loss of the best fixed action above each round's minimum. A follow-the-regularised-leader (FTRL) algorithm
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