Second-Moment Stochastic Approximation Methods
Classical stochastic approximation methods rely on estimators of the first moment (mean) of a random regression function. We study methods that employ estimators of both the first and the second moments, which include modern deep-learning optimizers such as Adam and Muon as special cases. We derive second-moment stochastic approximation methods through the lens of optimal preconditioning for solving matrix equations, and develop a two-stage framework for their convergence analysis. The first stage focuses on the analysis of conceptual (impractical) methods that rely on the exact first and second moments. In the second stage, we replace the exact moments with their respective estimators, a...
| Authors | Tao Jiang, Lin Xiao |
|---|---|
| Primary category | math.OC |
| Published | 29 September 2026 |
| Last updated at source | 29 September 2026 |
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