Adam-SHANG: A Convergent Adam-Type Method for Stochastic Smooth Convex Optimization
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. Experimen...
| Authors | Yaxin Yu, Long Chen, Minfu Feng |
|---|---|
| Primary category | math.OC |
| Published | 13 May 2026 |
| Last updated at source | 13 May 2026 |
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