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Gradient directions and relative inexactness in optimization and machine learning

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arxiv 2407.00667 v1 pith:YBBXT7MN submitted 2024-06-30 math.OC

Artem Vasin This is my paper · ORCID
classification math.OC
keywords gradientlearningmachinenoiserelativeacuteamplitudeangle
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In this paper, we investigate the influence of noise giving an estimate of the gradient having a acute angle with the original. Noise amplitude has a relative model. The work offers both theoretical calculations and theorems, as well as experimental results. Classic machine learning problems were chosen as experiments -- linear and logistic regression, computer vision and natural language processing.

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  1. Worst-case convergence analysis of relatively inexact gradient descent on smooth convex functions

    math.OC 2025-06 conditional novelty 6.0 of 10

    For smooth convex functions, relatively inexact gradient descent has a three-regime worst-case one-step rate, and the largest provably safe stepsize is 2/(1+delta).

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