A Van Trees Lower Bound for Fully Interactive Differentially Private Federated Learning

2026-07-09 · Source: cs.LG updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Cybersecurity & Data Privacy · Depth: Expert, long

Summary

This research establishes a general lower bound for differentially private federated learning protocols with arbitrary public-transcript interactions and local sample reuse across rounds. It introduces a federated van Trees lower bound for parameter estimation under squared ℓ₂ loss, applicable to any estimator satisfying a total clientwise sample-level zero-concentrated differential privacy (zCDP) constraint. The core technical contribution is a privacy-information contraction inequality for complete public transcripts. The bound's utility is demonstrated through applications to mean estimation, linear regression, and nonparametric regression, showing how heterogeneous client sample sizes (nₗ) and privacy budgets (ρₗ) influence the minimax lower bound via a harmonic sum of clientwise information contributions. This framework also recovers known lower bounds for central and local DP models.

Key takeaway

For AI Scientists and Research Scientists designing or evaluating federated learning protocols, this work provides a critical tool for understanding privacy-utility trade-offs. You can use the general federated van Trees lower bound to quantify the minimum achievable error under zCDP constraints, even with complex interactive protocols and local sample reuse. This allows you to benchmark your private federated learning algorithms against fundamental limits, ensuring your designs optimally balance privacy budgets and model accuracy.

Key insights

A general federated van Trees lower bound quantifies privacy-utility trade-offs in interactive differentially private federated learning.

Principles

• Client information contribution is limited by privacy or sample size.
• Heterogeneous client budgets affect minimax lower bounds.
• zCDP allows arbitrary adaptivity and sample reuse.

Method

The method establishes a federated van Trees lower bound using a privacy-information contraction inequality for complete public transcripts, simplifying computation compared to problem-specific score attacks.

In practice

• Apply the bound to mean estimation problems.
• Use for linear regression analysis.
• Extend to nonparametric regression models.

Topics

• Federated Learning
• Differential Privacy
• Zero-Concentrated DP
• Lower Bounds
• Van Trees Inequality
• Parameter Estimation
• Information Theory

Best for: AI Scientist, Research Scientist

Related on AIssential

• Statistical Limits and Efficient Algorithms for Differentially Private Federated Learning — New methods improve federated learning accuracy and communication efficiency while preserving differential privacy.
• Minimax Quantile Lower Bounds for Interactive Statistical Decision Making with Privacy — The paper develops a minimax-quantile theory for ISDM that accounts for rare failures and integrates MI privacy.
• Differentially Private Natural Gradient Descent — DP-NGD improves differentially private training utility and convergence by integrating curvature-aware optimization while mitigating privacy and stability challenges.
• What's in a Smoothness Constant? Tighter Rates for Local SGD with Bounded Second-order Heterogeneity — Bounded second-order heterogeneity explains Local SGD's efficiency across general convex objectives, with new tighter convergence bounds.
• Giskard : Byzantine Robust and Confidential Aggregation for Large-Scale Decentralized Learning — Giskard enables scalable, confidential, and Byzantine-robust decentralized learning aggregation using a tree-based committee structure and MPC.
• PAC-Bayesian Generalization Guarantees for Fairness on Stochastic and Deterministic Classifiers — PAC-Bayesian bounds can guarantee fairness for both stochastic and deterministic classifiers.

See Counsel's argued verdicts on the open AI decisions leaders are weighing →

Open in AIssential →

Editorial summary, takeaway, and curation by AIssential. Original article published by cs.LG updates on arXiv.org.