ניתוח התכנסות של שיטות רדיוס עם גזירה ורעש

תקציר מקורי באנגליתarXiv:2609.12119v1 Announce Type: new Abstract: Stochastic gradient descent (SGD) with gradient clipping and additive noise has become a standard technique for training machine learning models, particularly in applications requiring robustness or privacy guarantees. However, clipping introduces a bias in stochastic gradients, while additive noise introduces additional variance, making the long-run behaviour of individual optimization trajectories difficult to characterize. In this work, we prove that SGD with clipping and additive Gaussian noise (SGD-CN) converges almost surely (a.s.) under smoothness and uniformly bounded stochastic-gradient noise assumptions, provided the step sizes satisfy some standard decaying conditions. Our analysis extends to momentum variants such as the stochasti