A Stochastic Levenberg--Marquardt Method Using Random Models with Complexity Results

Globally convergent variants of the Gauss--Newton algorithm are often methods choice to tackle nonlinear least-squares problems. Among such frameworks, Levenberg--Marquardt and trust-region two well-established, similar paradigms. Both schemes have been studied when model is replaced by a random that only accurate with given probability. Trust-region also applied problems where objective value subject noise: this setting particular interest in fields as data assimilation, efficient can adapt noise needed account for intrinsic uncertainty input data. In paper, we describe stochastic handles noisy function values models, provided sufficient accuracy achieved Our method relies on specific scaling regularization parameter allows us leverage existing results algorithms. Moreover, exploit structure our through use family stationarity criteria tailored Provided probability estimates models sufficiently large, bound expected number iterations reach an approximate stationary point, which generalizes based using deterministic or noiseless values. We illustrate link between approach several applications related inverse machine learning.