Bring Your Own Algorithm for Optimal Differentially Private Stochastic Minimax Optimization

TL;DR

This paper introduces a flexible framework for differentially private stochastic minimax optimization that allows practitioners to use their own algorithms, achieving near-linear time complexity and near-optimal privacy-utility trade-offs.

Contribution

The authors develop a general, adaptable framework for DP-SMO that enables the use of various base algorithms, achieving near-linear time complexity and optimal privacy-utility trade-offs.

Findings

First near-linear time algorithms with near-optimal guarantees for smooth DP-SMO.

Framework allows use of sophisticated variance-reduced accelerated methods.

Enriches the family of near-linear time algorithms for smooth DP-SCO.

Abstract

We study differentially private (DP) algorithms for smooth stochastic minimax optimization, with stochastic minimization as a byproduct. The holy grail of these settings is to guarantee the optimal trade-off between the privacy and the excess population loss, using an algorithm with a linear time-complexity in the number of training samples. We provide a general framework for solving differentially private stochastic minimax optimization (DP-SMO) problems, which enables the practitioners to bring their own base optimization algorithm and use it as a black-box to obtain the near-optimal privacy-loss trade-off. Our framework is inspired from the recently proposed Phased-ERM method [22] for nonsmooth differentially private stochastic convex optimization (DP-SCO), which exploits the stability of the empirical risk minimization (ERM) for the privacy guarantee. The flexibility of our approach enables us to sidestep the requirement that the base algorithm needs to have bounded sensitivity, and allows the use of sophisticated variance-reduced accelerated methods to achieve near-linear time-complexity. To the best of our knowledge, these are the first near-linear time algorithms with near-optimal guarantees on the population duality gap for smooth DP-SMO, when the objective is (strongly-)convex--(strongly-)concave. Additionally, based on our flexible framework, we enrich the family of near-linear time algorithms for smooth DP-SCO with the near-optimal privacy-loss trade-off.