Differential Privacy via Distributionally Robust Optimization

要約

タイトル：分散ロバスト最適化を介した差分プライバシー
要約：
– 差分プライバシーが、個人のプライバシーを保護しながらデータセットの統計情報を共有するためのデファクトスタンダードとなっている
– 統計情報をランダムに歪ませることで、プライバシー-精度のトレードオフが生じる
– この分野において、最適なメカニズムは、予め選択したプライバシーレベルに対して最高の精度を提供するものである
– この論文は、分布的にロバストな最適化問題としてメカニズムの設計問題を定式化し、非漸近的かつ無条件的な最適性保証を持つメカニズムを開発することを提案する
– この問題は強力なデュアルを持ち、有限次元の上界と下界の収束的階層を開発することができる
– 数秒で解決できる切断面技術を用いた両方の境界問題を解くことができる
– 数値実験により、本論文の提案メカニズムが従来のベストインクラスの結果を上回ることが示された

要約(オリジナル)

In recent years, differential privacy has emerged as the de facto standard for sharing statistics of datasets while limiting the disclosure of private information about the involved individuals. This is achieved by randomly perturbing the statistics to be published, which in turn leads to a privacy-accuracy trade-off: larger perturbations provide stronger privacy guarantees, but they result in less accurate statistics that offer lower utility to the recipients. Of particular interest are therefore optimal mechanisms that provide the highest accuracy for a pre-selected level of privacy. To date, work in this area has focused on specifying families of perturbations a priori and subsequently proving their asymptotic and/or best-in-class optimality. In this paper, we develop a class of mechanisms that enjoy non-asymptotic and unconditional optimality guarantees. To this end, we formulate the mechanism design problem as an infinite-dimensional distributionally robust optimization problem. We show that the problem affords a strong dual, and we exploit this duality to develop converging hierarchies of finite-dimensional upper and lower bounding problems. Our upper (primal) bounds correspond to implementable perturbations whose suboptimality can be bounded by our lower (dual) bounds. Both bounding problems can be solved within seconds via cutting plane techniques that exploit the inherent problem structure. Our numerical experiments demonstrate that our perturbations can outperform the previously best results from the literature on artificial as well as standard benchmark problems.

arxiv情報

提供元, 利用サービス

arxiv.jp, OpenAI