A Stochastic Iteratively Regularized Gauss-Newton Method
<|reference_start|>A Stochastic Iteratively Regularized Gauss-Newton Method: 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.<|reference_end|>
@article{bergou2024a,
    title={A Stochastic Iteratively Regularized Gauss-Newton Method},
    author={El Houcine Bergou, Neil K. Chada, Youssef Diouane},
    journal={arXiv preprint arXiv:2409.12381},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.12381},
    primaryClass={math.NA cs.NA math.OC}
}