# On robustness and local differential privacy

arXiv: https://arxiv.org/abs/2201.00751 · HTML: https://mlsanity.com/paper/2201.00751/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jan 2022.

## Built on by (most cited first, 15 of 15)

- [Robustness Implies Privacy in Statistical Estimation](https://mlsanity.com/paper/2212.05015/) (2022)
- [DP-PCA: Statistically Optimal and Differentially Private PCA](https://mlsanity.com/paper/2205.13709/) (2022)
- [On the Privacy-Robustness-Utility Trilemma in Distributed Learning](https://mlsanity.com/paper/2302.04787/) (2023)
- [A Huber Loss Minimization Approach to Mean Estimation under User-level Differential Privacy](https://mlsanity.com/paper/2405.13453/) (2024)
- [A Unified Theoretical Analysis of Private and Robust Offline Alignment: from RLHF to DPO](https://mlsanity.com/paper/2505.15694/) (2025)
- [Robust Kernel Hypothesis Testing under Data Corruption](https://mlsanity.com/paper/2405.19912/) (2024)
- [On Private and Robust Bandits](https://mlsanity.com/paper/2302.02526/) (2023)
- [Robust Estimation of Discrete Distributions under Local Differential Privacy](https://mlsanity.com/paper/2202.06825/) (2022)
- [Learning with User-Level Local Differential Privacy](https://mlsanity.com/paper/2405.17079/) (2024)
- [Review of Mathematical Optimization in Federated Learning](https://mlsanity.com/paper/2412.01630/) (2024)
- [SquarechiPO: Differentially Private and Robust chi2-Preference Optimization in Offline Direct Alignment](https://mlsanity.com/paper/2505.21395/) (2025)
- [Differentially Private Statistical Inference through β-Divergence One Posterior Sampling](https://mlsanity.com/paper/2307.05194/) (2023)
- [On Theoretical Limits of Learning with Label Differential Privacy](https://mlsanity.com/paper/2502.14309/) (2025)
- [High-Dimensional Differentially Private Quantile Regression: Distributed Estimation and Statistical Inference](https://mlsanity.com/paper/2508.05212/) (2025)
- [Robust and differentially private stochastic linear bandits](https://mlsanity.com/paper/2304.11741/) (2023)

## Abstract (arXiv)

It is of soaring demand to develop statistical analysis tools that are robust against contamination as well as preserving individual data owners' privacy. In spite of the fact that both topics host a rich body of literature, to the best of our knowledge, we are the first to systematically study the connections between the optimality under Huber's contamination model and the local differential privacy (LDP) constraints. In this paper, we start with a general minimax lower bound result, which disentangles the costs of being robust against Huber's contamination and preserving LDP. We further study four concrete examples: a two-point testing problem, a potentially-diverging mean estimation problem, a nonparametric density estimation problem and a univariate median estimation problem. For each problem, we demonstrate procedures that are optimal in the presence of both contamination and LDP constraints, comment on the connections with the state-of-the-art methods that are only studied under either contamination or privacy constraints, and unveil the connections between robustness and LDP via partially answering whether LDP procedures are robust and whether robust procedures can be efficiently privatised. Overall, our work showcases a promising prospect of joint study for robustness and local differential privacy.