TY - JOUR
T1 - Near Optimal Methods for Minimizing Convex Functions with Lipschitz p-th Derivatives
AU - Gasnikov, Alexander
AU - Dvurechensky, Pavel
AU - Gorbunov, Eduard
AU - Vorontsova, Evgeniya
AU - Selikhanovych, Daniil
AU - Uribe, César A.
AU - Jiang, Bo
AU - Wang, Haoyue
AU - Zhang, Shuzhong
AU - Bubeck, Sébastien
AU - Jiang, Qijia
AU - Lee, Yin Tat
AU - Li, Yuanzhi
AU - Sidford, Aaron
N1 - Publisher Copyright:
© 2019 A. Gasnikov et al.
PY - 2019
Y1 - 2019
N2 - 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 ε approximate minimizer in O (ε - 2/3p+1) iterations. These methods match known lower bounds up to poly-logarithmic factors for constant p.
AB - 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 ε approximate minimizer in O (ε - 2/3p+1) iterations. These methods match known lower bounds up to poly-logarithmic factors for constant p.
UR - https://www.scopus.com/pages/publications/85160854483
UR - https://www.scopus.com/pages/publications/85160854483#tab=citedBy
M3 - Conference article
AN - SCOPUS:85160854483
SN - 2640-3498
VL - 99
SP - 1392
EP - 1393
JO - Proceedings of Machine Learning Research
JF - Proceedings of Machine Learning Research
T2 - 32nd Conference on Learning Theory, COLT 2019
Y2 - 25 June 2019 through 28 June 2019
ER -