We give new differentially private algorithms for the classic problems of learning decision lists and large-margin halfspaces in the PAC and online models. In the PAC model, we give a computationally efficient algorithm for learning decision lists with minimal sample overhead over the best non-private algorithms. In the online model, we give a private analog of the influential Winnow algorithm for learning halfspaces with mistake bound polylogarithmic in the dimension and inverse polynomial in the margin. As an application, we describe how to privately learn decision lists in the online model, qualitatively matching state-of-the art non-private guarantees.

翻译：本文针对PAC模型和在线模型中的经典决策列表学习与大间隔半空间学习问题，提出了新的差分隐私算法。在PAC模型中，我们提出了一种计算高效的决策列表学习算法，其样本复杂度相比最优非隐私算法仅存在最小限度的额外开销。在在线模型中，我们提出了具有影响力的Winnow算法的隐私版本，用于学习半空间，其错误界限在维度上为多对数级，在间隔上为逆多项式级。作为应用，我们描述了如何在在线模型中差分隐私地学习决策列表，其性能在质量上达到了最先进的非隐私算法保证。