# On the Generalization Properties of Differential Privacy

arXiv: https://arxiv.org/abs/1504.05800 · HTML: https://mlsanity.com/paper/1504.05800/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Apr 2015.

## Built on by (most cited first, 5 of 5)

- [On the Privacy Properties of GAN-generated Samples](https://mlsanity.com/paper/2206.01349/) (2022)
- [OmniForce: On Human-Centered, Large Model Empowered and Cloud-Edge Collaborative AutoML System](https://mlsanity.com/paper/2303.00501/) (2023)
- [FedEmb: A Vertical and Hybrid Federated Learning Algorithm using Network And Feature Embedding Aggregation](https://mlsanity.com/paper/2312.00102/) (2023)
- [A Theoretical Survey on Foundation Models](https://mlsanity.com/paper/2410.11444/) (2024)
- [Laplace Sample Information: Data Informativeness Through a Bayesian Lens](https://mlsanity.com/paper/2505.15303/) (2025)

## Abstract (arXiv)

A new line of work, started with Dwork et al., studies the task of answering statistical queries using a sample and relates the problem to the concept of differential privacy. By the Hoeffding bound, a sample of size O(log k/α2) suffices to answer k non-adaptive queries within error α, where the answers are computed by evaluating the statistical queries on the sample. This argument fails when the queries are chosen adaptively (and can hence depend on the sample). Dwork et al. showed that if the answers are computed with (ε,δ)-differential privacy then O(ε) accuracy is guaranteed with probability 1-O(δε). Using the Private Multiplicative Weights mechanism, they concluded that the sample size can still grow polylogarithmically with the k. Very recently, Bassily et al. presented an improved bound and showed that (a variant of) the private multiplicative weights algorithm can answer k adaptively chosen statistical queries using sample complexity that grows logarithmically in k. However, their results no longer hold for every differentially private algorithm, and require modifying the private multiplicative weights algorithm in order to obtain their high probability bounds. We greatly simplify the results of Dwork et al. and improve on the bound by showing that differential privacy guarantees O(ε) accuracy with probability 1-O(δlog(1/ε)/ε). It would be tempting to guess that an (ε,δ)-differentially private computation should guarantee O(ε) accuracy with probability 1-O(δ). However, we show that this is not the case, and that our bound is tight (up to logarithmic factors).