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3568. Advancing the lower bounds: An accelerated, stochastic, second-order method with optimal adaptation to inexactness

Invited abstract in session WB-32: Beyond First-Order Optimization Methods, stream Advances in large scale nonlinear optimization.

Wednesday, 10:30-12:00
Room: 41 (building: 303A)

Authors (first author is the speaker)

1.	Artem Agafonov
	Machine Learning, MBZUAI
2.	Dmitry Kamzolov
	Machine Learning, Mohamed bin Zayed University of Artificial Intelligence (MBZUAI)
3.	Alexander Gasnikov
	Mathematical Foundation of Control, Moscow Institute of Physics and Technology
4.	Ali Kavis
	ECE Department, University of Texas at Austin
5.	Kimon Antonakopoulos
	EPFL
6.	Volkan Cevher
	School of Engineering, EPFL
7.	Martin Takac
	Lehigh University

Abstract

We present a new accelerated stochastic second-order method that is robust to both gradient and Hessian inexactness, which occurs typically in machine learning. We establish theoretical lower bounds and prove that our algorithm achieves optimal convergence in both gradient and Hessian inexactness in this key setting. We further introduce a tensor generalization for stochastic higher-order derivatives. When the oracles are non-stochastic, the proposed tensor algorithm matches the global convergence of Nesterov Accelerated Tensor method. Both algorithms allow for approximate solutions of their auxiliary subproblems with verifiable conditions on the accuracy of the solution.

Keywords

• Convex Optimization

Status: accepted

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