Near Optimal Methods for Minimizing Convex Functions with Lipschitz -th Derivatives
A Gasnikov, P Dvurechensky… - … on Learning Theory, 2019 - proceedings.mlr.press
Conference on Learning Theory, 2019•proceedings.mlr.press
In this merged paper, we consider the problem of minimizing a convex function with
Lipschitz-continuous $ 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 $.
Lipschitz-continuous $ 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 $.
Abstract
In this merged paper, we consider the problem of minimizing a convex function with Lipschitz-continuous -th order derivatives. Given an oracle which when queried at a point returns the first -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 .
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