WIAS Preprint No. 2813, (2021)

Flexible modification of Gauss--Newton method and its stochastic extension


  • Yudin, Nikita
  • Gasnikov, Alexander

2020 Mathematics Subject Classification

  • 90C30 90C25 90C26


  • Systems of nonlinear equations, empirical risk minimization, Gauss--Newton method, trust region methods, non-convex optimization, inexact proximal mapping, inexact oracle, stochastic optimization, stochastic approximation, overparametrized model, weak growth condition, Polyak--Lojasiewicz condition, complexity estimate




This work presents a novel version of recently developed Gauss--Newton method for solving systems of nonlinear equations, based on upper bound of solution residual and quadratic regularization ideas. We obtained for such method global convergence bounds and under natural non-degeneracy assumptions we present local quadratic convergence results. We developed stochastic optimization algorithms for presented Gauss--Newton method and justified sub-linear and linear convergence rates for these algorithms using weak growth condition (WGC) and Polyak--Lojasiewicz (PL) inequality. We show that Gauss--Newton method in stochastic setting can effectively find solution under WGC and PL condition matching convergence rate of the deterministic optimization method. The suggested method unifies most practically used Gauss--Newton method modifications and can easily interpolate between them providing flexible and convenient method easily implementable using standard techniques of convex optimization.

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