April 4, 2024, 4:42 a.m. | Michael Menart, Enayat Ullah, Raman Arora, Raef Bassily, Crist\'obal Guzm\'an

cs.LG updates on arXiv.org arxiv.org

arXiv:2311.13447v2 Announce Type: replace
Abstract: We study private empirical risk minimization (ERM) problem for losses satisfying the $(\gamma,\kappa)$-Kurdyka-{\L}ojasiewicz (KL) condition. The Polyak-{\L}ojasiewicz (PL) condition is a special case of this condition when $\kappa=2$. Specifically, we study this problem under the constraint of $\rho$ zero-concentrated differential privacy (zCDP). When $\kappa\in[1,2]$ and the loss function is Lipschitz and smooth over a sufficiently large region, we provide a new algorithm based on variance reduced gradient descent that achieves the rate $\tilde{O}\big(\big(\frac{\sqrt{d}}{n\sqrt{\rho}}\big)^\kappa\big)$ on the …

abstract arxiv case cs.cr cs.lg differential differential privacy erm losses math.oc optimization privacy risk stat.ml study type

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