Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2605.18656

Statistical Limits and Efficient Algorithms for Differentially Private Federated Learning

Arnab Auddy·Xiangni Peng·Subhadeep Paul
View original source ↗Read source document ↗Export metadata ↓

Abstract

Federated Learning is a leading framework for training ML and AI models collaboratively across numerous user devices or databases. We study the trade-offs among estimation accuracy, privacy constraints, and communication cost for differentially private (DP) federated M estimation. The two standard methods in the literature are FedAvg, which may suffer from high federation bias, and FedSGD, which can incur high communication cost. Aimed at improving accuracy at a reduced communication cost, we propose FedHybrid, which uses FedSGD starting with an improved initialization by the FedAvg estimator. We propose FedNewton, which averages local Newton iterations to reduce bias in FedAvg, achieving an estimation accuracy comparable to FedSGD with much fewer communication rounds when the number of clients grows sufficiently slowly. We establish finite sample upper bounds on the mean-squared error rates of the DP versions of these estimators as functions of the number of clients, local sample sizes, privacy budget, and number of iterations. We further derive a minimax lower bound on the MSE of any iterative private federated procedure that provides a benchmark to assess the optimality gap of these methods. We numerically evaluate our methods for training a logistic regression and a neural network on the computer vision datasets MNIST and CIFAR-10.

Explore related subjects

stat.MLcs.AIcs.LGstat.ME

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Arnab Auddy, Xiangni Peng, Subhadeep Paul. 2026-05-18. Statistical Limits and Efficient Algorithms for Differentially Private Federated Learning. https://arxiv.org/abs/2605.18656

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Attack-Resistant Uniform Fairness for Linear and Smooth Contextual Bandits

Modern digital platforms use contextual bandits to allocate valuable exposure and opportunities among competing participants. Fair treatment is therefore an important concern, yet reward maximization alone does not ensure that preferential allocation reflects participants' merits. We develop algorithms for linear and smooth contextual bandits under uniform merit-based fairness, requiring the reward ordering to justify preferential allocation across all contexts and rounds, and study how these guarantees are affected by adversarial reward corruption. Our algorithms achieve \((1-\widetilde O(1/T))\)-fairness, with regret that is minimax optimal among fair policies for linear rewards and nearly minimax optimal for smooth rewards. In the linear setting, matching lower bounds identify the price of fairness exactly: minimax regret increases from \(\log T\) to \(\log^2 T\). For smooth rewards, the cost of fairness is at most polylogarithmic. We further establish a separation between regret and fairness robustness: an \(\widetilde O(1)\) corruption budget can cause substantial fairness violations without worsening the regret order. We therefore develop robust algorithms that adapt sampling, estimation, and fairness certification to corruption, which preserve uniform fairness and achieve minimax-optimal and nearly optimal regrets for linear and smooth rewards, respectively. Numerical and semi-synthetic experiments illustrate these findings.

stat.ML↗
arXiv2026

The Cost of Privacy: Rates of Convergence for Parameter Estimation with Differential Privacy

We study the minimax cost of $(\varepsilon,δ)$-differential privacy for mean estimation and Gaussian linear regression in low and high dimensions. For low-dimensional mean estimation, a resampling reduction to fingerprinting yields the privacy contribution $d^2\log(1/δ)/(n^2\varepsilon^2)$ in the stated polynomial-$δ$ regime. For low-dimensional regression, a tracing argument gives the contribution $d^2/(n^2\varepsilon^2)$ under an explicit approximate-DP remainder condition. For sparse mean estimation and sparse regression, a constant-weight packing and a private Fano lemma produce an effective privacy entropy of order $\min\{s\log(ed/s),[\log((e^\varepsilon-1)/δ)]_+\}$ for $δ>0$, up to universal constants and a fixed threshold; for pure DP it is $s\log(ed/s)$. Thus, when $δ$ is polynomially smaller than $\varepsilon$, the pure-DP dependence is retained up to polylogarithmic factors whenever the effective dimension is polylogarithmic in $n$, including regimes with $\varepsilon=o(1)$. Coordinatewise-clipping estimators for means and split-sample noisy-gradient estimators for regression attain the lower bounds up to explicit logarithmic factors. Simulations and data examples illustrate related implementations.

stat.ML↗
arXiv2026

Robust Mixture Models for Algorithmic Fairness Under Latent Heterogeneity

Machine learning models optimized for average performance can perform poorly on vulnerable subpopulations. Existing approaches often rely on groups specified in advance, yet fairness-relevant subgroup structure may be latent, intersectional, and driven by complex interactions among continuous and discrete attributes. We introduce \textbf{ROME} (\textbf{\underline{RO}}bust \textbf{\underline{M}}ixture \textbf{\underline{E}}nsemble), a framework that learns latent group structure while optimizing worst-group predictive performance. ROME connects latent-variable modeling with distributionally robust optimization (DRO) through two complementary approaches: an Expectation-Maximization formulation with robust aggregation for linear models and a neural Mixture-of-Experts formulation for nonlinear settings. Across simulations and three real-world regression datasets, ROME improves worst-group performance while maintaining competitive overall accuracy, including in comparisons with established group-aware and group-label-free robust learning methods. ROME provides a flexible approach to robust prediction when fairness-relevant attributes are available for subgroup discovery but their direct use in group-specific outcome models is restricted.

stat.ML↗