# Striking a Balance: An Optimal Mechanism Design for Heterogenous Differentially Private Data Acquisition for Logistic Regression

arXiv: https://arxiv.org/abs/2309.10340 · HTML: https://mlsanity.com/paper/2309.10340/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 55 references that are in the map.
- First posted on arXiv 19 Sep 2023.

## Builds on (most cited first, 20 of 20)

- [Collecting Telemetry Data Privately](https://mlsanity.com/paper/1712.01524/) (2017)
- [Privately Learning High-Dimensional Distributions](https://mlsanity.com/paper/1805.00216/) (2018)
- [Differentially Private Contextual Linear Bandits](https://mlsanity.com/paper/1810.00068/) (2018)
- [Private Mean Estimation of Heavy-Tailed Distributions](https://mlsanity.com/paper/2002.09464/) (2020)
- [Hierarchical Model-Based Imitation Learning for Planning in Autonomous Driving](https://mlsanity.com/paper/2210.09539/) (2022)
- [Heterogeneous Differential Privacy](https://mlsanity.com/paper/1504.06998/) (2015)
- [Optimum Statistical Estimation with Strategic Data Sources](https://mlsanity.com/paper/1408.2539/) (2014)
- [Optimal and Differentially Private Data Acquisition: Central and Local Mechanisms](https://mlsanity.com/paper/2201.03968/) (2022)
- [Accuracy First: Selecting a Differential Privacy Level for Accuracy-Constrained ERM](https://mlsanity.com/paper/1705.10829/) (2017)
- [Redrawing the Boundaries on Purchasing Data from Privacy-Sensitive Individuals](https://mlsanity.com/paper/1401.4092/) (2014)
- [Optimal Data Acquisition for Statistical Estimation](https://mlsanity.com/paper/1711.01295/) (2017)
- [Buying Private Data without Verification](https://mlsanity.com/paper/1404.6003/) (2014)
- [Sequential Peer Prediction: Learning to Elicit Effort using Posted Prices](https://mlsanity.com/paper/1611.09219/) (2016)
- [Prior-free Data Acquisition for Accurate Statistical Estimation](https://mlsanity.com/paper/1811.12655/) (2018)
- [Differentially Private LQ Control](https://mlsanity.com/paper/1807.05082/) (2018)
- [Buying Data Over Time: Approximately Optimal Strategies for Dynamic Data-Driven Decisions](https://mlsanity.com/paper/2101.07304/) (2021)
- [Optimal Dynamic Mechanism Design with Stochastic Supply and Flexible Consumers](https://mlsanity.com/paper/2007.03007/) (2020)
- [Privacy-Utility Trade-Offs Against Limited Adversaries](https://mlsanity.com/paper/2106.14643/) (2021)
- [Truthful Generalized Linear Models](https://mlsanity.com/paper/2209.07815/) (2022)
- [A Tractable Truthful Profit Maximization Mechanism Design with Autonomous Agents](https://mlsanity.com/paper/2302.05677/) (2023)

## Built on by (most cited first, 3 of 3)

- [Provable Mutual Benefits from Federated Learning in Privacy-Sensitive Domains](https://mlsanity.com/paper/2403.06672/) (2024)
- [Private Estimation when Data and Privacy Demands are Correlated](https://mlsanity.com/paper/2407.11274/) (2024)
- [Managing Correlations in Data and Privacy Demand](https://mlsanity.com/paper/2509.02856/) (2025)

## Abstract (arXiv)

We address the challenge of solving machine learning tasks using data from privacy-sensitive sellers. Since the data is private, we design a data market that incentivizes sellers to provide their data in exchange for payments. Therefore our objective is to design a mechanism that optimizes a weighted combination of test loss, seller privacy, and payment, striking a balance between building a good privacy-preserving ML model and minimizing payments to the sellers. To achieve this, we first propose an approach to solve logistic regression with known heterogeneous differential privacy guarantees. Building on these results and leveraging standard mechanism design theory, we develop a two-step optimization framework. We further extend this approach to an online algorithm that handles the sequential arrival of sellers.