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Quasi-Newton Methods for Machine Learning: Forget the Past, Just Sample
Optimization Methods and Software
  • Albert S. Berahas, University of Michigan, Ann Arbor
  • Majid Jahani, Lehigh University
  • Peter Richtárik, King Abdullah University of Science and Technology
  • Martin Takáč, Mohamed Bin Zayed University of Artificial Intelligence
Document Type

We present two sampled quasi-Newton methods (sampled LBFGS and sampled LSR1) for solving empirical risk minimization problems that arise in machine learning. Contrary to the classical variants of these methods that sequentially build Hessian or inverse Hessian approximations as the optimization progresses, our proposed methods sample points randomly around the current iterate at every iteration to produce these approximations. As a result, the approximations constructed make use of more reliable (recent and local) information and do not depend on past iterate information that could be significantly stale. Our proposed algorithms are efficient in terms of accessed data points (epochs) and have enough concurrency to take advantage of parallel/distributed computing environments. We provide convergence guarantees for our proposed methods. Numerical tests on a toy classification problem as well as on popular benchmarking binary classification and neural network training tasks reveal that the methods outperform their classical variants.

Publication Date
  • curvature pairs,
  • deep learning,
  • machine learning,
  • Quasi-Newton,
  • sampling

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Citation Information
A. S. Berahas, M. Jahani, P. Richtárik, and M. Takáč, “Quasi-Newton methods for machine learning: forget the past, just sample,” Optimization Methods and Software, 2021, doi: 10.1080/10556788.2021.1977806.