Research map / Federated learning and privacy / Differential privacy
Locally Optimal Private Sampling: Beyond the Global Minimax
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Extends the global minimax private sampler framework to functional LDP and shows that the local minimax sampler over a neighborhood of a reference distribution P0 is the global optimal sampler restricted to that neighborhood, with a pointwise better non-linear pure-LDP variant.
Problem
Private sampling under local differential privacy: generating one sample close to a client's distribution P in f-divergence while satisfying LDP; prior work optimizes worst-case (global) risk, which is pessimistic when real distributions are not worst-case.
Approach
Define a local minimax risk over a neighborhood N_gamma(P0) defined by zero hockey-stick divergence, show it equals the global minimax risk restricted to that neighborhood, extend global samplers to functional LDP (approximate, Gaussian), and derive a pointwise better non-linear clipping-based pure-LDP sampler.
Key results
- On a finite domain with k=20 and pure LDP, the local minimax sampler achieves lower worst-case f-divergence than the global minimax sampler across all epsilon and f-divergences tested.
- On a 1-D Laplace mixture (100 client distributions), the local sampler consistently achieves lower empirical worst-case f-divergence than the global sampler across epsilon values.
- The local minimax risk over N_gamma(P0) equals the global minimax risk restricted to that neighborhood, and the non-linear pure-LDP sampler is pointwise at least as good as the linear one (Proposition on instance-wise comparison).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the locally minimax sampler instead of the global minimax sampler | Private sampling on a finite sample space [k] (k = 20) · Finite sample space [k] | f-divergence | Helped |
| Use the locally minimax sampler instead of the global minimax sampler | Private sampling over a 1-D Laplace mixture · Continuous sample space (100 client distributions) | worst-case f-divergence | Helped |
| Use the nonlinear clipped sampler instead of the linear sampler | Locally private sampling for P in Nγ(P₀) · Nγ(P₀) | f-divergence | Helped |
| Use the locally optimal sampler instead of the global sampler | Private sampling under pure LDP and ν-GLDP · Numerical experiments | f-divergence | Helped |
Limitations
- Experiments are only on synthetic data (finite uniform reference and 1-D Laplace mixtures); no high-dimensional real-world evaluation.
- Clipping operation is computationally complex and scales poorly to high dimensions.
- Local neighborhood is restricted to zero E_gamma neighborhoods and single-sample-per-client setting.
Experimental setup
Metrics: worst-case f-divergence (KL, TV, squared Hellinger)
Baselines: global minimax linear sampler (Park et al. 2024) global functional LDP sampler
Builds on: Park et al. (NeurIPS'24) global minimax private sampler functional LDP (Dong et al.)
Closest papers by meaning
- Exactly Minimax-Optimal Locally Differentially Private Sampling (NeurIPS 2024 · similarity 0.94)
- Instance-Optimality for Private KL Distribution Estimation (NeurIPS 2025 · similarity 0.91)
- Minimax Optimal Two-Sample Testing under Local Differential Privacy (NeurIPS 2026 · similarity 0.91)
- On Inherent Privacy of Posterior Sampling: A Unified R\'enyi-Divergence Framework (NeurIPS 2026 · similarity 0.89)
- Tuning-free Estimation and Inference of Cumulative Distribution Function under Local Differential Privacy (ICML 2024 · similarity 0.89)
- Privacy Guarantees in Posterior Sampling under Contamination (NeurIPS 2026 · similarity 0.89)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.