Stability and Generalization of Differentially Private Minimax Problems

TL;DR

This paper investigates the privacy and generalization properties of differentially private algorithms in minimax problems, providing theoretical analysis under strongly-convex-strongly-concave conditions, a novel contribution in the field.

Contribution

It introduces the first theoretical analysis of the generalization performance of differentially private minimax algorithms under specific convexity conditions.

Findings

Provides high probability bounds on generalization error.

Establishes stability-based analysis for privacy guarantees.

First to analyze privacy in general minimax settings.

Abstract

In the field of machine learning, many problems can be formulated as the minimax problem, including reinforcement learning, generative adversarial networks, to just name a few. So the minimax problem has attracted a huge amount of attentions from researchers in recent decades. However, there is relatively little work on studying the privacy of the general minimax paradigm. In this paper, we focus on the privacy of the general minimax setting, combining differential privacy together with minimax optimization paradigm. Besides, via algorithmic stability theory, we theoretically analyze the high probability generalization performance of the differentially private minimax algorithm under the strongly-convex-strongly-concave condition. To the best of our knowledge, this is the first time to analyze the generalization performance of general minimax paradigm, taking differential privacy into account.