Geometric Moment Contraction for Stochastic Nesterov Acceleration

arXiv:2609.31303 · stat.ML, cs.LG · Submitted 2026-09-25 · Read on arXiv

stat.ML, cs.LG

Submitted: 2026-09-25

Updated: 2026-09-25

Project page: https://jiaqili97.github.io/research.html

Terminology

• Benchmark — 12× in this paper · explained in 2 episodes
• Adam — 4× in this paper · explained in 2 episodes
• Verification — 4× in this paper · explained in 2 episodes
• Generalization — 3× in this paper · explained in 13 episodes
• Robustness — 3× in this paper · explained in 5 episodes
• Trace — 3× in this paper · explained in 2 episodes
• Wasserstein Distance — 3× in this paper · explained in 4 episodes
• Adaptivity — 1× in this paper · explained in 1 episode
• Algorithmic Stability — 1× in this paper · explained in 1 episode
• Clustering — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Langevin Dynamics — 1× in this paper · explained in 2 episodes
• Non-asymptotic Analysis — 1× in this paper · explained in 2 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Sample Complexity — 1× in this paper · explained in 15 episodes

Sources

• A Polyak-Ruppert Central Limit Theorem for SA-Adam with Momentum and Non-Convergent Adaptive Preconditioning
• Limit Theorems for Stochastic Gradient Descent with Infinite Variance
• Statistical Inference for Stochastic Gradient Descent: Beyond Finite Variance
• Algorithmic Stability of Stochastic Gradient Descent with Momentum under Heavy-Tailed Noise
• The Anytime Convergence of Stochastic Gradient Descent with Momentum: From a Continuous-Time Perspective
• Strong error analysis for the stochastic momentum optimizer
• Nesterov acceleration in benignly non-convex landscapes
• Stochastic Gradient Descent with Momentum is Algorithmically Stable
• Revisiting the central limit theorems for the SGD-type methods
• Convergence and concentration properties of constant step-size SGD through Markov chains
• Acceleration of stochastic gradient descent with momentum by averaging: finite-sample rates and asymptotic normality
• Generalized Stochastic Gradient Descent with Momentum Methods for Smooth Optimization
• Unified Convergence Analysis of Stochastic Momentum Methods for Convex and Non-convex Optimization
• SHANG++: Robust Stochastic Acceleration under Multiplicative Noise
• Delayed supermartingale convergence lemmas for stochastic approximation with Nesterov momentum

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