Adam-SHANG: A Convergent Adam-Type Method for Stochastic Smooth Convex Optimization

Fuente: arXiv
Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Yu, Yaxin, Chen, Long, Feng, Minfu
Format: Preprint
Veröffentlicht: 2026
Schlagworte:
Online-Zugang:
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
_version_ 1866918498620407808
author Yu, Yaxin
Chen, Long
Feng, Minfu
author_facet Yu, Yaxin
Chen, Long
Feng, Minfu
contents We propose Adam-SHANG, a Lyapunov-guided Adam-type method that couples momentum, adaptive preconditioning, and a curvature-aware correction through a more stable lagged-preconditioner update. For stochastic smooth convex optimization, we prove convergence in expectation under an admissible stepsize condition that can always be satisfied by a conservative spectral bound, without imposing global monotonicity on the second-moment sequence. To obtain a less conservative practical rule, we introduce a computable trace-ratio stepsize, motivated by a local coordinatewise alignment condition. The same structural update is also tested beyond the convex setting with simplified parameters. Experiments validate the predicted stochastic decay and show competitive training performance against Adam and AdamW on deep learning tasks.
format Preprint
id arxiv_https___arxiv_org_abs_2605_12878
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Adam-SHANG: A Convergent Adam-Type Method for Stochastic Smooth Convex Optimization
Yu, Yaxin
Chen, Long
Feng, Minfu
Optimization and Control
Machine Learning
We propose Adam-SHANG, a Lyapunov-guided Adam-type method that couples momentum, adaptive preconditioning, and a curvature-aware correction through a more stable lagged-preconditioner update. For stochastic smooth convex optimization, we prove convergence in expectation under an admissible stepsize condition that can always be satisfied by a conservative spectral bound, without imposing global monotonicity on the second-moment sequence. To obtain a less conservative practical rule, we introduce a computable trace-ratio stepsize, motivated by a local coordinatewise alignment condition. The same structural update is also tested beyond the convex setting with simplified parameters. Experiments validate the predicted stochastic decay and show competitive training performance against Adam and AdamW on deep learning tasks.
title Adam-SHANG: A Convergent Adam-Type Method for Stochastic Smooth Convex Optimization
topic Optimization and Control
Machine Learning
url https://arxiv.org/abs/2605.12878