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arXiv 1906.09613cs.LGcs.CRstat.ML
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The Cost of a Reductions Approach to Private Fair Optimization

Harvard University(哈佛大学);School of Engineering and Applied Sciences(工程与应用科学学院)

Daniel Alabi

英文摘要:

Through the lens of information-theoretic reductions, we examine a reductions approach to fair optimization and learning where a black-box optimizer is used to learn a fair model for classification or regression. Quantifying the complexity, both statistically and computationally, of making such models satisfy the rigorous definition of differential privacy is our end goal. We resolve a few open questions and show applicability to fair machine learning, hypothesis testing, and to optimizing non-standard measures of classification loss. Furthermore, our sample complexity bounds are tight amongst all strategies that jointly minimize a composition of functions. The reductions approach to fair optimization can be abstracted as the constrained group-objective optimization problem where we aim to optimize an objective that is a function of losses of individual groups, subject to some constraints. We give the first polynomial-time algorithms to solve the problem with $(ε, 0)$ or $(ε, δ)$ differential privacy guarantees when defined on a convex decision set (for example, the $\ell_P$ unit ball) with convex constraints and losses. Accompanying information-theoretic lower bounds for the problem are presented. In addition, compared to a previous method for ensuring differential privacy subject to a relaxed form of the equalized odds fairness constraint, the $(ε, δ)$-differentially private algorithm we present provides asymptotically better sample complexity guarantees, resulting in an exponential improvement in certain parameter regimes. We introduce a class of bounded divergence linear optimizers, which could be of independent interest, and specialize to pure and approximate differential privacy.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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