Privacy Odometers and Filters: Pay-as-you-Go Composition

In this paper we initiate the study of adaptive composition in differential privacy when the length of the composition, and the privacy parameters themselves can be chosen adaptively, as a function of the outcome of previously run analyses. This case is much more delicate than the setting covered by existing composition theorems, in which the algorithms themselves can be chosen adaptively, but the privacy parameters must be fixed up front. Indeed, it isn’t even clear how to define differential privacy in the adaptive parameter setting. We proceed by defining two objects which cover the two main use cases of composition theorems. A privacy filter is a stopping time rule that allows an analyst to halt a computation before his pre-specified privacy budget is exceeded. A privacy odometer allows the analyst to track realized privacy loss as he goes, without needing to pre-specify a privacy budget. We show that unlike the case in which privacy parameters are fixed, in the adaptive parameter setting, these two use cases are distinct. We show that there exist privacy filters with bounds comparable (up to constants) with existing privacy composition theorems. We also give a privacy odometer that nearly matches non-adaptive private composition theorems, but is sometimes worse by a small asymptotic factor. Moreover, we show that this is inherent, and that any valid privacy odometer in the adaptive parameter setting must lose this factor, which shows a formal separation between the filter and odometer use-cases. ∗Department of Applied Mathematics and Computational Science, University of Pennsylvania. [email protected]. †Department of Computer and Information Sciences, University of Pennsylvania. [email protected]. Supported in part by an NSF CAREER award, NSF grant CNS-1513694, and a grant from the Sloan Foundation. ‡College of Computer and Information Science, Northeastern University. [email protected] §Center for Research on Computation & Society and John A. Paulson School of Engineering & Applied Sciences, Harvard University. [email protected]. Work done while visiting the Department of Applied Mathematics and the Shing-Tung Yau Center at National Chiao-Tung University in Taiwan. Also supported by NSF grant CNS-1237235, a grant from the Sloan Foundation, and a Simons Investigator Award. 1 ar X iv :1 60 5. 08 29 4v 2 [ cs .C R ] 1 J un 2 01 6