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The paradigm of Differentially Private SGD~(DP-SGD) can provide a theoreticalguarantee for training data in both centralized and federated settings.However, the utility degradation caused by DP-SGD limits its wide applicationin high-stakes tasks, such as medical image diagnosis. In addition to thenecessary perturbation, the convergence issue is attributed to the informationloss on the gradient clipping. In this work, we propose a general frameworkPCDP-SGD, which aims to compress redundant gradient norms and preserve morecrucial top gradient components via projection operation before gradientclipping. Additionally, we extend PCDP-SGD as a fundamental component indifferential privacy federated learning~(DPFL) for mitigating the dataheterogeneous challenge and achieving efficient communication. We prove thatpre-projection enhances the convergence of DP-SGD by reducing the dependence ofclipping error and bias to a fraction of the top gradient eigenspace, and intheory, limits cross-client variance to improve the convergence underheterogeneous federation. Experimental results demonstrate that PCDP-SGDachieves higher accuracy compared with state-of-the-art DP-SGD variants incomputer vision tasks. Moreover, PCDP-SGD outperforms current federatedlearning frameworks when DP is guaranteed on local training sets.

PCDP-SGD: Improving the Convergence of Differentially Private SGD via Projection in Advance