Stability and Generalization of Differentially Private Minimax Problems
This work addresses privacy concerns for minimax problems in machine learning, which is important for applications like reinforcement learning and GANs, but it is incremental as it extends existing differential privacy and stability theory to a new setting.
The paper tackles the lack of privacy analysis in general minimax problems by combining differential privacy with minimax optimization, and theoretically analyzes the high-probability generalization performance under strongly-convex-strongly-concave conditions, providing the first such analysis in this context.
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.