SAN: Stochastic Average Newton Algorithm for Minimizing Finite Sums
| Title: | SAN: Stochastic Average Newton Algorithm for Minimizing Finite Sums |
|---|---|
| Authors: | Chen, Jiabin, Yuan, Rui, Garrigos, Guillaume, Gower, Robert M. |
| Source: | Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:279-318, 2022 |
| Publication Year: | 2021 |
| Collection: | Computer Science Mathematics |
| Subject Terms: | Mathematics - Optimization and Control, Mathematics - Numerical Analysis |
| More Details: | We present a principled approach for designing stochastic Newton methods for solving finite sum optimization problems. Our approach has two steps. First, we re-write the stationarity conditions as a system of nonlinear equations that associates each data point to a new row. Second, we apply a Subsampled Newton Raphson method to solve this system of nonlinear equations. Using our approach, we develop a new Stochastic Average Newton (SAN) method, which is incremental by design, in that it requires only a single data point per iteration. It is also cheap to implement when solving regularized generalized linear models, with a cost per iteration of the order of the number of the parameters. We show through extensive numerical experiments that SAN requires no knowledge about the problem, neither parameter tuning, while remaining competitive as compared to classical variance reduced gradient methods (e.g. SAG and SVRG), incremental Newton and quasi-Newton methods (e.g. SNM, IQN). Comment: Accepted at AISTATS 2022 |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/2106.10520 |
| Accession Number: | edsarx.2106.10520 |
| Database: | arXiv |
| Description not available. |