Doubly Adaptive Scaled Algorithm for Machine Learning Using Second-Order Information

Authors

Majid Jahani, Lehigh University
Sergey Rusakov, Lehigh University
Zheng Shi, Lehigh University
Peter Richtárik, KAUSTFollow
Michael W. Mahoney, University of California, Berkeley
Martin Takáč, Mohamed bin Zayed University of Artificial IntelligenceFollow

Document Type

Article

Publication Title

arXiv

Abstract

We present a novel adaptive optimization algorithm for large-scale machine learning problems. Equipped with a low-cost estimate of local curvature and Lipschitz smoothness, our method dynamically adapts the search direction and step-size. The search direction contains gradient information preconditioned by a well-scaled diagonal preconditioning matrix that captures the local curvature information. Our methodology does not require the tedious task of learning rate tuning, as the learning rate is updated automatically without adding an extra hyperparameter. We provide convergence guarantees on a comprehensive collection of optimization problems, including convex, strongly convex, and nonconvex problems, in both deterministic and stochastic regimes. We also conduct an extensive empirical evaluation on standard machine learning problems, justifying our algorithm's versatility and demonstrating its strong performance compared to other start-of-the-art first-order and second-order methods. Copyright © 2021, The Authors. All rights reserved.

DOI

10.48550/arXiv.2109.05198

Publication Date

9-11-2021

Keywords

Optimization and Control

Comments

Preprint: arXiv

Recommended Citation

M. Jahani, S. Rusakov, Z. Shi, P. Richtárik, M. W. Mahoney, and M. Takáč "Doubly adaptive scaled algorithm for machine learning using second-order information," 2021, arXiv:2109.05198