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On the asymptotic rate of convergence of Stochastic Newton algorithms and their Weighted Averaged versions

Claire Boyer () and Antoine Godichon-Baggioni ()
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Claire Boyer: Sorbonne-Université
Antoine Godichon-Baggioni: Sorbonne-Université

Computational Optimization and Applications, 2023, vol. 84, issue 3, No 8, 972 pages

Abstract: Abstract Most machine learning methods can be regarded as the minimization of an unavailable risk function. To optimize the latter, with samples provided in a streaming fashion, we define general (weighted averaged) stochastic Newton algorithms, for which a theoretical analysis of their asymptotic efficiency is conducted. The corresponding implementations are shown not to require the inversion of a Hessian estimate at each iteration under a quite flexible framework that covers the case of linear, logistic or softmax regressions to name a few. Numerical experiments on simulated and real data give the empirical evidence of the pertinence of the proposed methods, which outperform popular competitors particularly in case of bad initializations.

Keywords: Stochastic optimization; Newton algorithm; Averaged stochastic algorithm; Online learning (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10589-022-00442-3

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