Gaussian Differential Privacy

Differential privacy has seen remarkable success as a rigorous and practical formalization of data privacy in the past decade. This privacy definition and its divergence based relaxations, however, have several acknowledged weaknesses, either in handling composition of private algorithms or in analyzing important primitives like privacy amplification by subsampling. Inspired by the hypothesis testing formulation of privacy, this paper proposes a new relaxation, which we term `$f$-differential privacy' ($f$-DP). This notion of privacy has a number of appealing properties and, in particular, avoids difficulties associated with divergence based relaxations. First, $f$-DP preserves the hypothesis testing interpretation. In addition, $f$-DP allows for lossless reasoning about composition in an algebraic fashion. Moreover, we provide a powerful technique to import existing results proven for original DP to $f$-DP and, as an application, obtain a simple subsampling theorem for $f$-DP. In addition to the above findings, we introduce a canonical single-parameter family of privacy notions within the $f$-DP class that is referred to as `Gaussian differential privacy' (GDP), defined based on testing two shifted Gaussians. GDP is focal among the $f$-DP class because of a central limit theorem we prove. More precisely, the privacy guarantees of \emph{any} hypothesis testing based definition of privacy (including original DP) converges to GDP in the limit under composition. The CLT also yields a computationally inexpensive tool for analyzing the exact composition of private algorithms. Taken together, this collection of attractive properties render $f$-DP a mathematically coherent, analytically tractable, and versatile framework for private data analysis. Finally, we demonstrate the use of the tools we develop by giving an improved privacy analysis of noisy stochastic gradient descent.

Equilibrium Characterization for Data Acquisition Games

We study a game between two firms in which each provide a service based on machine learning. The firms are presented with the opportunity to purchase a new corpus of data, which will allow them to potentially improve the quality of their products. The firms can decide whether or not they want to buy the data, as well as which learning model to build with that data. We demonstrate a reduction from this potentially complicated action space to a one-shot, two-action game in which each firm only decides whether or not to buy the data. The game admits several regimes which depend on the relative strength of the two firms at the outset and the price at which the data is being offered. We analyze the game's Nash equilibria in all parameter regimes and demonstrate that, in expectation, the outcome of the game is that the initially stronger firm's market position weakens whereas the initially weaker firm's market position becomes stronger. Finally, we consider the perspective of the users of the service and demonstrate that the expected outcome at equilibrium is not the one which maximizes the welfare of the consumers.

Strategic Classification from Revealed Preferences

We study an online linear classification problem, in which the data is generated by strategic agents who manipulate their features in an effort to change the classification outcome. In rounds, the learner deploys a classifier, and an adversarially chosen agent arrives, possibly manipulating her features to optimally respond to the learner. The learner has no knowledge of the agents' utility functions or "real" features, which may vary widely across agents. Instead, the learner is only able to observe their "revealed preferences" --- i.e. the actual manipulated feature vectors they provide. For a broad family of agent cost functions, we give a computationally efficient learning algorithm that is able to obtain diminishing "Stackelberg regret" --- a form of policy regret that guarantees that the learner is obtaining loss nearly as small as that of the best classifier in hindsight, even allowing for the fact that agents will best-respond differently to the optimal classifier.