Sub-sampled Newton methods


For large-scale finite-sum minimization problems, we study non-asymptotic and high-probability global as well as local convergence properties of variants of Newton’s method where the Hessian and/or gradients are randomly sub-sampled. For Hessian sub-sampling, using random matrix concentration inequalities, one can sub-sample in a way that second-order information, i.e., curvature, is suitably preserved. For gradient sub-sampling, approximate matrix multiplication results from randomized numerical linear algebra provide a way to construct the sub-sampled gradient which contains as much of the first-order information as possible. While sample sizes all depend on problem specific constants, e.g., condition number, we demonstrate that local convergence rates are problem-independent.

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Correspondence to Farbod Roosta-Khorasani.

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Roosta-Khorasani, F., Mahoney, M.W. Sub-sampled Newton methods. Math. Program. 174, 293–326 (2019).

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  • Newton-type methods
  • Local and global convergence
  • Sub-sampling

Mathematics Subject Classification

  • 49M15
  • 65K05
  • 90C25
  • 90C06