English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we study the application of quasi-Newton methods for solvingempirical risk minimization (ERM) problems defined over a large dataset.Traditional deterministic and stochastic quasi-Newton methods can be executedto solve such problems; however, it is known that their global convergence ratemay not be better than first-order methods, and their local superlinearconvergence only appears towards the end of the learning process. In thispaper, we use an adaptive sample size scheme that exploits the superlinearconvergence of quasi-Newton methods globally and throughout the entire learningprocess. The main idea of the proposed adaptive sample size algorithms is tostart with a small subset of data points and solve their corresponding ERMproblem within its statistical accuracy, and then enlarge the sample sizegeometrically and use the optimal solution of the problem corresponding to thesmaller set as an initial point for solving the subsequent ERM problem withmore samples. We show that if the initial sample size is sufficiently large andwe use quasi-Newton methods to solve each subproblem, the subproblems can besolved superlinearly fast (after at most three iterations), as we guaranteethat the iterates always stay within a neighborhood that quasi-Newton methodsconverge superlinearly. Numerical experiments on various datasets confirm ourtheoretical results and demonstrate the computational advantages of our method.

Exploiting Local Convergence of Quasi-Newton Methods Globally: Adaptive Sample Size Approach