Iterative algorithms, like gradient descent, are common tools for solving a variety of problems, such as model fitting. For this reason, there is interest in creating differentially private versions of them. However, their conversion to differentially private algorithms is often naive. For instance, a fixed number of iterations are chosen, the privacy budget is split evenly among them, and at each iteration, parameters are updated with a noisy gradient. In this paper, we show that gradient-based algorithms can be improved by a more careful allocation of privacy budget per iteration. Intuitively, at the beginning of the optimization, gradients are expected to be large, so that they do not need to be measured as accurately. However, as the parameters approach their optimal values, the gradients decrease and hence need to be measured more accurately. We add a basic line-search capability that helps the algorithm decide when more accurate gradient measurements are necessary. Our gradient descent algorithm works with the recently introduced zCDP version of differential privacy. It outperforms prior algorithms for model fitting and is competitive with the state-of-the-art for $(\epsilon,\delta)$-differential privacy, a strictly weaker definition than zCDP.

本文说明如何通过更加精心地分配每个迭代的隐私预算，从而改进基于梯度的算法，提高其对模型拟合的性能。

自适应每次迭代隐私预算的集中式差分隐私梯度下降