The Privacy Price of Tail-Risk Learning: Effective Tail Sample Size in Differentially Private CVaR Optimization
Authors: El Mustapha Mansouri
Summary
arXiv:2605. 16219v1 Announce Type: cross Abstract: Differential privacy changes the effective sample size governing CVaR learning.
Relevance
Read next because The Privacy Price of Tail-Risk Learning: Effective Tail Sample Size in Differentially Private CVaR Optimization overlaps with clean result "Leakage rate is a usable signal for recovering trigger-shaped phrases on Gaperon-1125-1B without knowing the hidden trigger itself (MODERATE confidence)", clean result "Language-mismatch LoRA SFT on Qwen2.5-7B leaks the trained completion language into bystander directives the model was never trained on, absent under same-language SFT (LOW confidence)", clean result "A pretraining-data-poisoned Qwen3-4B backdoor only fires on the exact trigger tokens — paraphrases don't activate it, and base-model similarity to the trigger doesn't predict which inputs fire (MODERATE confidence)". Matching terms: class, under, rate, position. Source: arxiv stat.ML (Machine Learning).
Abstract
arXiv:2605.16219v1 Announce Type: cross Abstract: Differential privacy changes the effective sample size governing CVaR learning. For tail mass $\tau$, the privacy-relevant sample size is not $n$, but $n\tau$; equivalently, the effective private tail sample size is $\epsilon n\tau$. Private CVaR excess risk decomposes into ordinary tail-risk statistical error and a privacy price. This decomposition is complete for scalar estimation and finite classes: scalar estimation has rate $\Theta(B \min{1,(n\tau)^{-1/2}+(\epsilon n\tau)^{-1}})$, and finite classes of size $M$ have rate $\Theta(B \min{1,\sqrt{\log(2M)/(n\tau)}+\log(2M)/(\epsilon n\tau)})$. These complete rates hold under pure DP, and their lower bounds extend to approximate DP in the stated small-$\delta$ regimes. For convex Lipschitz learning, modular upper and lower reductions show that the CVaR-specific privacy term necessarily scales as $1/(\epsilon n\tau)$, with dimension dependence inherited from private stochastic convex optimization. Together, these results identify ordinary private learning on $\Theta(n\tau)$ informative tail records as the canonical hard subproblem inside private CVaR learning.