Generalization and Optimization of SGD with Lookahead
This work addresses a theoretical gap for researchers and practitioners using the Lookahead optimizer in deep learning, though it is incremental as it builds on existing optimization methods.
The paper tackles the lack of theoretical understanding of the Lookahead optimizer's generalization capabilities by conducting a rigorous stability analysis, deriving generalization bounds for convex and strongly convex problems without restrictive assumptions, and showing a linear speedup with batch size in the convex setting.
The Lookahead optimizer enhances deep learning models by employing a dual-weight update mechanism, which has been shown to improve the performance of underlying optimizers such as SGD. However, most theoretical studies focus on its convergence on training data, leaving its generalization capabilities less understood. Existing generalization analyses are often limited by restrictive assumptions, such as requiring the loss function to be globally Lipschitz continuous, and their bounds do not fully capture the relationship between optimization and generalization. In this paper, we address these issues by conducting a rigorous stability and generalization analysis of the Lookahead optimizer with minibatch SGD. We leverage on-average model stability to derive generalization bounds for both convex and strongly convex problems without the restrictive Lipschitzness assumption. Our analysis demonstrates a linear speedup with respect to the batch size in the convex setting.