We introduce a new mechanism for stochastic convex optimization (SCO) with user-level differential privacy guarantees. The convergence rates of this mechanism are similar to those in the prior work of Levy et al. (2021); Narayanan et al. (2022), but with two important improvements. Our mechanism does not require any smoothness assumptions on the loss. Furthermore, our bounds are also the first where the minimum number of users needed for user-level privacy has no dependence on the dimension and only a logarithmic dependence on the desired excess error. The main idea underlying the new mechanism is to show that the optimizers of strongly convex losses have low local deletion sensitivity, along with an output perturbation method for functions with low local deletion sensitivity, which could be of independent interest.

翻译：我们提出了一种新的随机凸优化（SCO）机制，该机制具有用户级差分隐私保证。该机制的收敛速率与 Levy 等人（2021）和 Narayanan 等人（2022）先前的工作相似，但有两个重要改进。我们的机制不需要对损失函数做任何光滑性假设。此外，我们的界是首个具有如下性质的界：用户级隐私所需的最小用户数不依赖于维数，仅依赖于期望的过剩误差的对数。该新机制的核心思想在于证明强凸损失函数的优化器具有较低的局部删除敏感性，并结合一种针对低局部删除敏感性函数的输出扰动方法，这一方法可能具有独立的研究价值。