A Unified Lyapunov-IQC Framework for Uniform Stability of Smooth Quadratic First-Order Accelerated Optimizers
We develop a unified Lyapunov-integral quadratic constraint (IQC) framework for establishing uniform stability of first-order accelerated optimization algorithms in the $β$-smooth and $γ$-strongly convex regime. Classical analyses of uniform stability, such as the work of Hardt, Recht, and Singer for stochastic gradient descent (SGD), rely on direct coupling arguments and case-by-case control of iterate differences under random sampling. Extending such arguments to accelerated methods, such as Nesterov Accelerated Gradient (NAG), is complicated by the presence of higher-order state dynamics induced by momentum. We first extend this classical approach with the use of Lyapunov functions to ...
| Authors | Don Li, Dacian Daescu |
|---|---|
| Primary category | math.OC |
| Published | 8 May 2026 |
| Last updated at source | 1 July 2026 |
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