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Our4 results certify that there exists an optimal linear pre-conditioner for quadratically convex constraint sets. As such,5 adaptivegradient methods can be minimax (rate) optimal. Inonline algorithms, the common practice [4,5,6,7,2]6 is to measure regret with respect to the "best" post-hoc regularizer (i.e. In this setting, the constraint set corresponds to the set of classifiers of interest, and the geometry of the gradients34 corresponds tothegeometry ofthefeatures (orcovariates). A generalized online mirror descent with applications to classification and52 regression.