$f$-Differential Privacy Filters: Validity and Approximate Solutions

• URL: http://arxiv.org/abs/2602.06756v1
• Date: Fri, 06 Feb 2026 15:04:02 GMT
• Title: $f$-Differential Privacy Filters: Validity and Approximate Solutions
• Authors: Long Tran, Antti Koskela, Ossi Räisä, Antti Honkela,
• Abstract summary: Accounting for privacy loss under fully adaptive composition is a central challenge in differential privacy.<n>It remains unclear whether optimal trade-off-function-based notions, such as $f$-DP, admit valid privacy filters under fully adaptive interaction.
• Score: 10.451946278781007
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Accounting for privacy loss under fully adaptive composition -- where both the choice of mechanisms and their privacy parameters may depend on the entire history of prior outputs -- is a central challenge in differential privacy (DP). In this setting, privacy filters are stopping rules for compositions that ensure a prescribed global privacy budget is not exceeded. It remains unclear whether optimal trade-off-function-based notions, such as $f$-DP, admit valid privacy filters under fully adaptive interaction. We show that the natural approach to defining an $f$-DP filter -- composing individual trade-off curves and stopping when the prescribed $f$-DP curve is crossed -- is fundamentally invalid. We characterise when and why this failure occurs, and establish necessary and sufficient conditions under which the natural filter is valid. Furthermore, we prove a fully adaptive central limit theorem for $f$-DP and construct an approximate Gaussian DP filter for subsampled Gaussian mechanisms at small sampling rates $q<0.2$ and large sampling rates $q>0.8$, yielding tighter privacy guarantees than filters based on Rényi DP in the same setting.

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