Unveiling Lookahead’s Potential in Sharpness-Aware Minimization: Convergence and Generalization Revisited

Deep learning models have achieved remarkable success across various applications, but over-parameterized networks often suffer from overfitting and limited generalization, limiting their real-world performance. Sharpness-Aware Lookahead (SALA), which integrates Sharpness-Aware Minimization (SAM) with the lookahead mechanism, has been proposed to improve generalization, training stability, and convergence. However, recent theoretical studies suggest that lookahead may delay convergence, which appears to contradict empirical observations. This discrepancy raises a fundamental question: how does lookahead affect the generalization and optimization behavior of SAM? To answer this question, we develop a systematic theoretical framework to derive tighter generalization and excess risk bounds for SALA under relaxed assumptions. Our results show that the lookahead parameter $\alpha$ affects optimization and generalization in opposite directions: 1) the optimization bound $O(\frac{1}{(Tk+1{)}^{2\alpha }}+\frac{k}{(Tk+1{)}^{2\alpha -1}})$decays faster as $\alpha$ increases, while 2) the generalization bound $O(\frac{T^{\alpha }\log T}{n})$ increases with $\alpha$ through both the leading factor $\alpha$ and the power-law term $T^{\alpha }$. We present detailed comparisons with prior theoretical studies and empirical observations to support the validity of our findings. Furthermore, the analysis extended to the stochastic gradient descent-based lookahead algorithm uncovers a similar impact of lookahead on generalization and optimization behaviors from both theoretical and empirical perspectives.