{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/fast-and-furious-convergence-stochastic","title":"Fast and Furious Convergence: Stochastic Second Order Methods under Interpolation","arxiv_id":"1910.04920","date":"2019-10-11","proceeding":null,"authors":["Si Yi Meng","Sharan Vaswani","Issam Laradji","Mark Schmidt","Simon Lacoste-Julien"],"abstract":"We consider stochastic second-order methods for minimizing smooth and strongly-convex functions under an interpolation condition satisfied by over-parameterized models. Under this condition, we show that the regularized subsampled Newton method (R-SSN) achieves global linear convergence with an adaptive step-size and a constant batch-size. By growing the batch size for both the subsampled gradient and Hessian, we show that R-SSN can converge at a quadratic rate in a local neighbourhood of the solution. We also show that R-SSN attains local linear convergence for the family of self-concordant functions. Furthermore, we analyze stochastic BFGS algorithms in the interpolation setting and prove their global linear convergence. We empirically evaluate stochastic L-BFGS and a \"Hessian-free\" implementation of R-SSN for binary classification on synthetic, linearly-separable datasets and real datasets under a kernel mapping. Our experimental results demonstrate the fast convergence of these methods, both in terms of the number of iterations and wall-clock time.","url_abs":"https://arxiv.org/abs/1910.04920v2","url_pdf":"https://arxiv.org/pdf/1910.04920v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"fast-and-furious-convergence-stochastic","repo_url":"https://github.com/IssamLaradji/ssn","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"binary-classification","task_name":"Binary Classification"},{"task_slug":"second-order-methods","task_name":"Second-order methods"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1910.04920","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}