Minimax Data Sanitization with Distortion Constraint and Adversarial Inference

TL;DR

This paper introduces a minimax data sanitization framework that balances privacy and utility in a multi-adversary setting, using a constrained optimization approach with theoretical benchmarks.

Contribution

It formulates a novel minimax optimization problem for privacy-preserving data sharing with multiple adversaries and proposes a data-driven training method, including analytical solutions for Gaussian and binary cases.

Findings

Proposed a minimax data sanitization model with distortion constraints.

Developed an alternating training procedure for privatizer, reconstructor, and adversaries.

Provided theoretical benchmarks for Gaussian and binary data scenarios.

Abstract

We study a privacy-preserving data-sharing setting where a privatizer transforms private data into a sanitized version observed by an authorized reconstructor and two unauthorized adversaries, each with access to side information correlated with the private data. The reconstructor is evaluated under a distortion function, while each adversary is evaluated using a separate loss function. The privatizer ensures the reconstructor distortion remains below a fixed threshold while maximizing the minimum loss across the two adversaries. This two-adversary setting models cases where individual users cannot reconstruct the data accurately, but their combined side information enables estimation within the distortion threshold. The privatizer maximizes individual loss while permitting accurate reconstruction only through collaboration. This echoes secret-sharing principles, but with lossy rather than perfect recovery. We frame this as a constrained data-driven minimax optimization problem and propose a data-driven training procedure that alternately updates the privatizer, reconstructor, and adversaries. We also analyze the Gaussian and binary cases as special scenarios where optimal solutions can be obtained. These theoretical optimal results are benchmarks for evaluating the proposed minimax training approach.