arXiv Machine Learning By Sharan Sahu, Cameron J. Hogan, Martin T. Wells

On the Provable Suboptimality of Momentum SGD in Nonstationary Stochastic Optimization

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arXiv:2601. 12238v5 Announce Type: replace-cross Abstract: In this paper, we provide a comprehensive theoretical analysis of Stochastic Gradient Descent (SGD) and its momentum variants (Polyak Heavy-Ball and Nesterov) for tracking time-varying optima under strong convexity and smoothness.

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arXiv Machine Learning
Sep 14

Adapt or Forget: Provable Tradeoffs Between Adam and SGD in Nonstationary Optimization

The paper presents a theoretical study of Adam in non‑stationary stochastic optimization, distinguishing two regimes: Euclidean tracking under adaptive strong monotonicity and high‑probability projected stationarity for general smooth objectives. It derives finite‑time bounds that decompose into initialization, objective drift, first‑moment tracking error (β₁), and preconditioner perturbation (β₂), and characterizes burn‑in times for constant and step‑decay schedules. The analysis reveals a noise–drift tradeoff, showing that in noise‑dominated settings Adam’s adaptive mechanisms can improve guarantees, while in drift‑dominated settings they may worsen tracking, potentially making vanilla SGD preferable.

By Sharan Sahu, Abir Sarkar, Cameron J. Hogan, Martin T. Wells
arXiv Machine Learning
Aug 18

Adaptive Optimization via Momentum on Variance-Normalized Gradients

arXiv:2602. 10204v2 Announce Type: replace Abstract: We introduce MVN-Grad (Momentum on Variance-Normalized Gradients), an Adam-style optimizer that improves stability and performance by combining two complementary ideas: variance-based normalization and momentum applied after normalization.

By Francisco Patitucci, Aryan Mokhtari
arXiv Machine Learning
Sep 14

Almost Sure Convergence Analysis of Stochastic Gradient Methods with Clipping and Additive Noise

The paper proves that stochastic gradient descent with gradient clipping and additive Gaussian noise (SGD‑CN) converges almost surely under smoothness and bounded noise assumptions, given standard decaying step sizes. The analysis extends to momentum variants such as the stochastic heavy ball and Nesterov's accelerated gradient, showing that careful energy constructions yield similar guarantees. These results provide stronger theoretical foundations for understanding the pathwise behaviour of clipped stochastic gradient methods in both convex and nonconvex regimes.

By Amartya Mukherjee, Jun Liu