Near Optimal Methods for Minimizing Convex Functions with Lipschitz $p$th Derivatives
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Proceedings of the ThirtySecond Conference on Learning Theory, PMLR 99:13921393, 2019.
Abstract
In this merged paper, we consider the problem of minimizing a convex function with Lipschitzcontinuous $p$th order derivatives. Given an oracle which when queried at a point returns the first $p$derivatives of the function at that point we provide some methods which compute an $\e$ approximate minimizer in $O\left(\e^{\frac{2}{3p+1}} \right)$ iterations. These methods match known lower bounds up to polylogarithmic factors for constant $p$.
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