AI RESEARCH
Adam-SHANG: A Convergent Adam-Type Method for Stochastic Smooth Convex Optimization
arXiv CS.LG
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ArXi:2605.12878v1 Announce Type: cross We propose Adam-SHANG, a Lyapuno-guided Adam-type method that couples momentum, adaptive preconditioning, and a curvature-aware correction through a 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.