Non-Asymptotic Optimization and Generalization Bounds for Stochastic Gauss-Newton in Overparameterized Models
This work addresses the impact of higher-order optimization on generalization in deep learning, providing theoretical insights for researchers in optimization and machine learning, though it is incremental as it builds on existing methods.
The paper analyzes a stochastic Gauss-Newton method for training overparameterized deep neural networks, establishing finite-time convergence bounds and non-asymptotic generalization bounds that show how curvature and overparameterization affect performance.
An important question in deep learning is how higher-order optimization methods affect generalization. In this work, we analyze a stochastic Gauss-Newton (SGN) method with Levenberg-Marquardt damping and mini-batch sampling for training overparameterized deep neural networks with smooth activations in a regression setting. Our theoretical contributions are twofold. First, we establish finite-time convergence bounds via a variable-metric analysis in parameter space, with explicit dependencies on the batch size, network width and depth. Second, we derive non-asymptotic generalization bounds for SGN using uniform stability in the overparameterized regime, characterizing the impact of curvature, batch size, and overparameterization on generalization performance. Our theoretical results identify a favorable generalization regime for SGN in which a larger minimum eigenvalue of the Gauss-Newton matrix along the optimization path yields tighter stability bounds.