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Privacy Profiles for Private Selection
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Derives (epsilon,delta) privacy-profile bounds for private selection (ReportNoisyMax and randomized-count tuning) from the privacy profiles of base mechanisms, giving tighter accounting than RDP for DP-SGD tuning and generalized PTR.
Problem
Private selection (Report Noisy Max, Sparse Vector, private hyperparameter tuning) is analyzed mainly via RDP, which is lossy when (epsilon,delta)-DP is needed; there are no bounds that use base mechanisms' privacy profiles directly.
Approach
Bound the hockey-stick divergence of the best-of-K selection output using the base mechanism's privacy profile and the probability generating function of the random number of runs K; this yields point-wise (epsilon,delta) bounds for truncated negative binomial and binomial distributions of K, and also allows tuning of privacy-affecting hyperparameters.
Key results
- For Poisson-subsampled Gaussian DP-SGD (q=16384/50000, sigma=21.1, T=250), the new bound allows approximately 3 times as many candidate models as the RDP bound.
- For the geometric case (eta=1), selecting from (epsilon,delta)-DP base mechanisms gives (3epsilon + m delta, m delta)-DP, improving on the 3epsilon pure bound from prior work.
- For generalized PTR tuning on UCI linear regression, the new bounds improve the privacy-utility trade-off over baselines including OPS-Balanced and output perturbation.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use privacy-profile accounting instead of RDP accounting | Private hyperparameter tuning of DP-SGD · DP-SGD tuning, q=16384/50000, σ=21.1, T=250 | candidate models evaluated: approximately 3 times as many models | Helped |
| Tune σ using geometrically distributed K | Poisson-subsampled Gaussian mechanism · DP-SGD tuning, q=0.01, σ=2.0, 3.0, and 4.0 | iterations: ≈ 4000, 10000 and 18000 iterations | Helped |
| Use the privacy-profile bound rather than RDP accounting | Private selection with a binomial number of runs · Gaussian mechanism, sensitivity 1, σ=4.0, m=10 | concentration of K at δ ≈ 10^-6: δ ≈ 10^{-6} | Helped |
Limitations
- Results for binomial K require a condition relating epsilon_1 and delta(epsilon_1), and the binomial bound approximates Poisson only as n grows.
- Accounting for Gaussian-like base profiles is shown in figures, with the bound for DP-SGD relying on numerical accountants and dominating pairs.
- Bounds for the Sparse Vector case are not developed in the body text despite being named in the abstract.
Experimental setup
Datasets: UCI benchmark datasets (linear regression)
Benchmarks: UCI linear regression (two datasets)
Metrics: epsilon-delta privacy bound privacy-utility trade-off number of evaluable models
Baselines: RDP-based private selection bounds Poisson-distributed K RDP bound OPS-Balanced output perturbation 3-epsilon pure DP selection bound
Builds on: Renyi differential privacy Liu and Talwar private selection Papernot and Steinke private selection Generalized Propose-Test-Release DP-SGD
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