Federated Learning of Quantile Inference under Local Differential Privacy

2025-09-25

AI Summary

This paper addresses quantile inference in federated learning under local differential privacy (LDP). To handle data heterogeneity and personalized privacy budgets, we propose a communication-efficient and statistically optimal framework: a robust estimator based on local stochastic gradient descent (Local SGD) for the nonsmooth quantile loss; the first asymptotic normality and functional central limit theorem for such estimators under LDP constraints; and a self-normalized inference procedure that constructs confidence intervals without auxiliary parameter estimation. Theoretically, the estimator achieves the minimax optimal statistical efficiency under LDP. Empirically, it attains high estimation accuracy, strong privacy protection (with ε ≤ 2), and low communication overhead on both synthetic and real-world datasets.

Technology Category

• Machine Learning: Privacy
• Search and Optimization: Local Search
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

In this paper, we investigate federated learning for quantile inference under local differential privacy (LDP). We propose an estimator based on local stochastic gradient descent (SGD), whose local gradients are perturbed via a randomized mechanism with global parameters, making the procedure tolerant of communication and storage constraints without compromising statistical efficiency. Although the quantile loss and its corresponding gradient do not satisfy standard smoothness conditions typically assumed in existing literature, we establish asymptotic normality for our estimator as well as a functional central limit theorem. The proposed method accommodates data heterogeneity and allows each server to operate with an individual privacy budget. Furthermore, we construct confidence intervals for the target value through a self-normalization approach, thereby circumventing the need to estimate additional nuisance parameters. Extensive numerical experiments and real data application validate the theoretical guarantees of the proposed methodology.

Problem

• Federated quantile inference under local differential privacy
• Handling non-smooth quantile loss with asymptotic normality
• Constructing confidence intervals without nuisance parameter estimation

Innovation

• Federated learning with local differential privacy
• Local SGD with perturbed gradients mechanism
• Self-normalization for confidence intervals construction