A Unified Lyapunov-IQC Framework for Uniform Stability of Smooth Quadratic First-Order Accelerated Optimizers
arXiv:2605.08488v2 Announce Type: replace-cross Abstract: We develop a unified Lyapunov-integral quadratic constraint (IQC) framework for establishing uniform stability of first-order accelerated optimization algorithms in the $\beta$-smooth and $\gamma$-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
The continuous drive for more efficient and robust optimization algorithms in AI, particularly for complex models, motivates advanced theoretical frameworks to ensure stability and performance.
A unified mathematical framework for understanding and ensuring the stability of accelerated optimization methods enhances the reliability and predictability of AI model training, crucial for deploying large-scale systems.
This research provides a more generalized and rigorous method for analyzing the uniform stability of a class of optimization algorithms, potentially leading to more robust and higher-performing AI systems.
- · AI researchers and algorithm developers
- · Deep learning practitioners
- · Companies deploying large-scale AI models
Improved theoretical guarantees for AI optimization algorithms will lead to more stable and faster convergence in training complex models.
Enhanced algorithm stability could reduce computational resources and time needed for hyperparameter tuning and model development.
More robust and efficient training could accelerate advances in AI capabilities across various applications, from agents to scientific discovery.
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Read at arXiv cs.LG