Ordinary Nonconvex SGD under Distance-Dependent Moments: Finite-Horizon Stationarity and Nagaev Bounds

arXiv:2609.30499 · stat.ML, cs.LG · Submitted 2026-09-24 · Read on arXiv

stat.ML, cs.LG

Submitted: 2026-09-24

Updated: 2026-10-07

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Accuracy — 3× in this paper · explained in 1 episode
• Hilbert Space — 3× in this paper · explained in 2 episodes
• Verification — 3× in this paper · explained in 2 episodes
• Admissibility — 2× in this paper · explained in 2 episodes
• Adaptivity — 1× in this paper · explained in 1 episode
• Convergence Guarantees — 1× in this paper · explained in 3 episodes
• Regularization — 1× in this paper · explained in 3 episodes

Sources

• Towards Weaker Variance Assumptions for Stochastic Optimization
• High-probability Bounds for Non-Convex Stochastic Optimization with Heavy Tails
• Provable convergence guarantees for black-box variational inference
• Lower Bounds and Proximally Anchored SGD for Non-Convex Minimization Under Unbounded Variance
• High Probability Convergence of Stochastic Gradient Methods
• Fuk-Nagaev inequality in smooth Banach spaces: Optimum bounds for distributions of heavy-tailed martingales
• Beyond Bounded Variance: Variance-Reduced Normalized Methods for Nonconvex Optimization under Blum-Gladyshev Noise

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