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arxiv: 2211.05727 · v1 · pith:FD4K7ZBQ · submitted 2022-11-10 · math.OC · cs.LG

A Randomised Subspace Gauss-Newton Method for Nonlinear Least-Squares

Coralia Cartis , Jaroslav Fowkes , Zhen Shao This is my paper

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classification math.OC cs.LG
keywords least-squaresnonlinearr-sgngauss-newtonpresentedproblemsrandomisedregression
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We propose a Randomised Subspace Gauss-Newton (R-SGN) algorithm for solving nonlinear least-squares optimization problems, that uses a sketched Jacobian of the residual in the variable domain and solves a reduced linear least-squares on each iteration. A sublinear global rate of convergence result is presented for a trust-region variant of R-SGN, with high probability, which matches deterministic counterpart results in the order of the accuracy tolerance. Promising preliminary numerical results are presented for R-SGN on logistic regression and on nonlinear regression problems from the CUTEst collection.

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