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Deep neural networks are often overparameterized and may not easily achieve model generalization. Adversarial training has shown effectiveness in improving generalization by regularizing the change of loss on top of adversarially chosen perturbations. The recently proposed sharpness-aware minimization (SAM) algorithm conducts adversarial weight perturbation, encouraging the model to converge to a flat minima. SAM finds a common adversarial weight perturbation per-batch. Although per-instance adversarial weight perturbations are stronger adversaries and can potentially lead to better generalization performance, their computational cost is very high and thus it is impossible to use per-instance perturbations efficiently in SAM. In this paper, we tackle this efficiency bottleneck and propose sharpness-aware minimization with dynamic reweighting (delta-SAM). Our theoretical analysis motivates that it is possible to approach the stronger, per-instance adversarial weight perturbations using reweighted per-batch weight perturbations. delta-SAM dynamically reweights perturbation within each batch according to the theoretically principled weighting factors, serving as a good approximation to per-instance perturbation. Experiments on various natural language understanding tasks demonstrate the effectiveness of delta-SAM.