aiqbench analysis
This research introduces Abstract Gradient Sampling (AGS), a formal method using abstract interpretation to tighten differential privacy guarantees for both private learning and unbounded regression tasks. By reducing parameterized model learning to a regression problem, the approach achieves finite privacy bounds in scenarios where global sensitivity is typically infinite, offering improved utility over standard baselines. The work advances theoretical machine learning by leveraging reachability-based analysis to establish more favorable privacy-utility trade-offs without relying on noise addition alone.
Certification-Based Differentially Private Learning
arXiv:2609.39629v1 Announce Type: new Abstract: Differential privacy (DP) in machine learning is typically achieved by adding noise to model parameters (private learning) or to model outputs (private prediction). Recent work uses formal methods, namely abstract interpretation, to provide tighter privacy guarantees, but only for private prediction in classification settings. In this work, we investigate the use of formal methods as a general tool for tighter privacy analysis. First, we generalize the abstract gradient training (AGT) framework to private prediction in continuous, unbounded regression. Second, by reducing learning in parameterized models to a regression problem over the parameter space, we introduce Abstract Gradient Sampling (AGS), an algorithm that enables reachability-based analysis to provide guarantees for private learning. In both private prediction and private learning, we provide tightened privacy accounting for the AGT framework and a theoretical analysis demonstrating when our smooth sensitivity upper-bounds yield favourable privacy-utility trade-off. In practice, we validate that our regression bounds are tighter than global-sensitivity baselines on regression benchmarks, and, notably, yield the first finite privacy guarantees in settings where global prediction sensitivity is a priori unbounded. We also find that under matched conditions, our private learning algorithm can outperform standard private learners.
Abstract:Differential privacy (DP) in machine learning is typically achieved by adding noise to model parameters (private learning) or to model outputs (private prediction). Recent work uses formal methods, namely abstract interpretation, to provide tighter privacy guarantees, but only for private prediction in classification settings. In this work, we investigate the use of formal methods as a general tool for tighter privacy analysis. First, we generalize the abstract gradient training (AGT) framework to private prediction in continuous, unbounded regression. Second, by reducing learning in parameterized models to a regression problem over the parameter space, we introduce Abstract Gradient Sampling (AGS), an algorithm that enables reachability-based analysis to provide guarantees for private learning. In both private prediction and private learning, we provide tightened privacy accounting for the AGT framework and a theoretical analysis demonstrating when our smooth sensitivity upper-bounds yield favourable privacy-utility trade-off. In practice, we validate that our regression bounds are tighter than global-sensitivity baselines on regression benchmarks, and, notably, yield the first finite privacy guarantees in settings where global prediction sensitivity is a priori unbounded. We also find that under matched conditions, our private learning algorithm can outperform standard private learners.
Machine Learning (cs.LG)
arXiv:2609.39629 [cs.LG]
(or arXiv:2609.39629v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.39629 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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