A Randomised Subspace Gauss-Newton Method for Nonlinear Least-Squares
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Abstract (arXiv)
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.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 9 of its 22 references that are in the map. First posted on arXiv 10 Nov 2022.
Builds on
9 of 22 references.
References · 9
- 2014OpenML: networked science in machine learningcited by 523
- 2014Sketching as a Tool for Numerical Linear Algebracited by 285
- 2015Newton Sketch: A Linear-time Optimization Algorithm with Linear-Quadratic Convergencecited by 72
- 2019RSN: Randomized Subspace Newtoncited by 34
- 2016Efficient Second Order Online Learning by Sketchingcited by 33
- 2015Global convergence rate analysis of unconstrained optimization methods based on probabilistic modelscited by 27
- 2015SDNA: Stochastic Dual Newton Ascent for Empirical Risk Minimizationcited by 18
- 2018Randomized Block Cubic Newton Methodcited by 14
- 2014Parallel Selective Algorithms for Big Data Optimizationcited by 6
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Citing papers per year: 2026: 2.
2 papers.