PAC learning with stable and private predictions

TL;DR

This paper introduces new algorithms for stable and private binary classification that significantly reduce sample complexity compared to previous methods, achieving near-optimal bounds for uniform stability and differential privacy.

Contribution

The paper presents novel algorithms for stable and private learning with improved sample complexity bounds, reducing overhead in PAC learning models.

Findings

Existence of a $ ilde O(d/(eta heta) + d/ heta^2)$ sample complexity bound for stable learning.

New algorithms for differentially private prediction with reduced sample requirements.

Bounds are nearly tight, matching or improving upon previous results.

Abstract

We study binary classification algorithms for which the prediction on any point is not too sensitive to individual examples in the dataset. Specifically, we consider the notions of uniform stability (Bousquet and Elisseeff, 2001) and prediction privacy (Dwork and Feldman, 2018). Previous work on these notions shows how they can be achieved in the standard PAC model via simple aggregation of models trained on disjoint subsets of data. Unfortunately, this approach leads to a significant overhead in terms of sample complexity. Here we demonstrate several general approaches to stable and private prediction that either eliminate or significantly reduce the overhead. Specifically, we demonstrate that for any class $C$ of VC dimension $d$ there exists a $\gamma$-uniformly stable algorithm for learning $C$ with excess error $\alpha$ using $\tilde O(d/(\alpha\gamma) + d/\alpha^2)$ samples. We also show that this bound is nearly tight. For $\epsilon$-differentially private prediction we give two new algorithms: one using $\tilde O(d/(\alpha^2\epsilon))$ samples and another one using $\tilde O(d^2/(\alpha\epsilon) + d/\alpha^2)$ samples. The best previously known bounds for these problems are $O(d/(\alpha^2\gamma))$ and $O(d/(\alpha^3\epsilon))$, respectively.