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arXiv · 2409.12381

A Stochastic Iteratively Regularized Gauss-Newton Method

El Houcine Bergou·Neil K. Chada·Youssef Diouane
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Abstract

This work focuses on developing and motivating a stochastic version of a wellknown inverse problem methodology. Specifically, we consider the iteratively regularized Gauss-Newton method, originally proposed by Bakushinskii for infinite-dimensional problems. Recent work have extended this method to handle sequential observations, rather than a single instance of the data, demonstrating notable improvements in reconstruction accuracy. In this paper, we further extend these methods to a stochastic framework through mini-batching, introducing a new algorithm, the stochastic iteratively regularized Gauss-Newton method (SIRGNM). Our algorithm is designed through the use randomized sketching. We provide an analysis for the SIRGNM, which includes a preliminary error decomposition and a convergence analysis, related to the residuals. We provide numerical experiments on a 2D elliptic PDE example. This illustrates the effectiveness of the SIRGNM, through maintaining a similar level of accuracy while reducing on the computational time.

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El Houcine Bergou, Neil K. Chada, Youssef Diouane. 2024-09-19. A Stochastic Iteratively Regularized Gauss-Newton Method. https://arxiv.org/abs/2409.12381

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