Minimax Optimality of Shampoo for Nonstationary Stochastic Optimization
We develop a comprehensive theoretical analysis of Matrix Shampoo for tracking time-varying optima in nonstationary stochastic optimization. We derive finite-horizon high-probability bounds for average tracking error that disentangle initialization, optimizer drift, momentum-induced drift penalty, stochastic noise, and adaptive preconditioning, with explicit dependence on momentum parameter \(β_1\) and stabilization parameter \(\varepsilon\). These bounds reveal an explicit drift--noise and stability--geometry tradeoffs: noise-dominated regimes favor larger $β_1$, which provides stronger first-moment averaging and greater suppression of gradient noise, whereas drift-dominated regimes favo...
| Authors | Abir Sarkar, Nirmalya Mandal, Martin T. Wells |
|---|---|
| Primary category | stat.ML |
| Published | 12 October 2026 |
| Last updated at source | 12 October 2026 |
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