Differentially Private algorithms often need to select the best amongst many candidate options. Classical works on this selection problem require that the candidates' goodness, measured as a real-valued score function, does not change by much when one person's data changes. In many applications such as hyperparameter optimization, this stability assumption is much too strong. In this work, we consider the selection problem under a much weaker stability assumption on the candidates, namely that the score functions are differentially private. Under this assumption, we present algorithms that are near-optimal along the three relevant dimensions: privacy, utility and computational efficiency. Our result can be seen as a generalization of the exponential mechanism and its existing generalizations. We also develop an online version of our algorithm, that can be seen as a generalization of the sparse vector technique to this weaker stability assumption. We show how our results imply better algorithms for hyperparameter selection in differentially private machine learning, as well as for adaptive data analysis.

本文考虑了在对候选项稳定性更弱的情况下，即评分函数是差分隐私的情况下的选择问题。我们提供了算法，在隐私、效用和计算效率等三个方面都是最优的。同时，我们还开发了在线版本和基于稀疏向量技术的通用性算法。这些算法在差分隐私机器学习中的超参数选择以及自适应数据分析中都有更好的表现。

私人候选人的私人选择