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.
|Original language||English (US)|
|Number of pages||37|
|Journal||Optimization Methods and Software|
|State||Published - Oct 15 2021|
Bibliographical noteKAUST Repository Item: Exported on 2021-10-19
Acknowledgements: This work was partially supported by the U.S. National Science Foundation, under award numbers NSF:CCF:1618717 and NSF:CCF:1740796, Defense Advanced Research Projects Agency (DARPA) Lagrange award PHR-001117S0039, and XSEDE Startup grant IRI180020.
ASJC Scopus subject areas
- Control and Optimization
- Applied Mathematics