Computer Science > Machine Learning
[Submitted on 11 Oct 2019 (v1), last revised 22 Mar 2020 (this version, v2)]
Title:Fast and Furious Convergence: Stochastic Second Order Methods under Interpolation
View PDFAbstract: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.
Submission history
From: Sharan Vaswani [view email][v1] Fri, 11 Oct 2019 00:24:19 UTC (1,324 KB)
[v2] Sun, 22 Mar 2020 21:47:56 UTC (3,524 KB)
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