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Differential privacy (DP) is a widely used notion for reasoning about privacywhen publishing aggregate data. In this paper, we observe that certain DPmechanisms are amenable to a posteriori privacy analysis that exploits the factthat some outputs leak less information about the input database than others.To exploit this phenomenon, we introduce output differential privacy (ODP) anda new composition experiment, and leverage these new constructs to obtainsignificant privacy budget savings and improved privacy-utility tradeoffs undercomposition. All of this comes at no cost in terms of privacy; we do not weakenthe privacy guarantee.  To demonstrate the applicability of our a posteriori privacy analysistechniques, we analyze two well-known mechanisms: the Sparse Vector Techniqueand the Propose-Test-Release framework. We then show how our techniques can beused to save privacy budget in more general contexts: when a differentiallyprivate iterative mechanism terminates before its maximal number of iterationsis reached, and when the output of a DP mechanism provides unsatisfactoryutility. Examples of the former include iterative optimization algorithms,whereas examples of the latter include training a machine learning model with alarge generalization error. Our techniques can be applied beyond the currentpaper to refine the analysis of existing DP mechanisms or guide the design offuture mechanisms.

Privacy accounting $\varepsilon$conomics: Improving differential privacy composition via a posteriori bounds