# Versatile Differentially Private Learning for General Loss Functions

arXiv: https://arxiv.org/abs/2501.15127 · HTML: https://mlsanity.com/paper/2501.15127/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jan 2025.

## Built on by (most cited first, 1 of 1)

- [How Much is Left? LLMs Linearly Encode Their Remaining Output Length](https://mlsanity.com/paper/2607.05316/) (2026)

## Abstract (arXiv)

This paper aims to provide a versatile privacy-preserving release mechanism along with a unified approach for subsequent parameter estimation and statistical inference. We propose the ZIL privacy mechanism based on zero-inflated symmetric multivariate Laplace noise, which requires no prior specification of subsequent analysis tasks, allows for general loss functions under minimal conditions, imposes no limit on the number of analyses, and is adaptable to the increasing data volume in online scenarios. We derive the trade-off function for the proposed ZIL mechanism that characterizes its privacy protection level. Within the M-estimation framework, we propose a novel doubly random corrected loss (DRCL) for the ZIL mechanism, which provides consistent and asymptotic normal M-estimates for the parameters of the target population under differential privacy constraints. The proposed approach is easy to compute without numerical integration and differentiation for noisy data. It is applicable for a general class of loss functions, including non-smooth loss functions like check loss and hinge loss. Simulation studies, including logistic regression and quantile regression, are conducted to evaluate the performance of the proposed method.