Training deep learning models with differential privacy (DP) results in a degradation of performance. The training dynamics of models with DP show a significant difference from standard training, whereas understanding the geometric properties of private learning remains largely unexplored. In this paper, we investigate sharpness, a key factor in achieving better generalization, in private learning. We show that flat minima can help reduce the negative effects of per-example gradient clipping and the addition of Gaussian noise. We then verify the effectiveness of Sharpness-Aware Minimization (SAM) for seeking flat minima in private learning. However, we also discover that SAM is detrimental to the privacy budget and computational time due to its two-step optimization. Thus, we propose a new sharpness-aware training method that mitigates the privacy-optimization trade-off. Our experimental results demonstrate that the proposed method improves the performance of deep learning models with DP from both scratch and fine-tuning. Code is available at https://github.com/jinseongP/DPSAT.
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