Differentially Private Bilevel Optimization

Guy Kornowski
Proceedings of The 37th International Conference on Algorithmic Learning Theory, PMLR 313:1-36, 2026.

Abstract

We present differentially private (DP) algorithms for bilevel optimization, a problem class that received significant attention lately in various machine learning applications. These are the first algorithms for such problems under standard DP constraints, and are also the first to avoid Hessian computations which are prohibitive in large-scale settings. Under the well-studied setting in which the upper-level is not necessarily convex and the lower-level problem is strongly-convex, our proposed gradient-based $(\epsilon,\delta)$-DP algorithm returns a point with hypergradient norm at most $\widetilde{\mathcal{O}}\left((\sqrt{d_\mathrm{up}}/\epsilon n)^{1/2}+(\sqrt{d_\mathrm{low}}/\epsilon n)^{1/3}\right)$ where $n$ is the dataset size, and $d_\mathrm{up}/d_\mathrm{low}$ are the upper/lower level dimensions. Our analysis covers constrained and unconstrained problems alike, accounts for mini-batch gradients, and applies to both empirical and population losses. As an application, we specialize our analysis to derive a simple private rule for tuning a regularization hyperparameter.

Cite this Paper

BibTeX
@InProceedings{pmlr-v313-kornowski26a, title = {Differentially Private Bilevel Optimization}, author = {Kornowski, Guy}, booktitle = {Proceedings of The 37th International Conference on Algorithmic Learning Theory}, pages = {1--36}, year = {2026}, editor = {Telgarsky, Matus and Ullman, Jonathan}, volume = {313}, series = {Proceedings of Machine Learning Research}, month = {23--26 Feb}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v313/main/assets/kornowski26a/kornowski26a.pdf}, url = {https://proceedings.mlr.press/v313/kornowski26a.html}, abstract = {We present differentially private (DP) algorithms for bilevel optimization, a problem class that received significant attention lately in various machine learning applications. These are the first algorithms for such problems under standard DP constraints, and are also the first to avoid Hessian computations which are prohibitive in large-scale settings. Under the well-studied setting in which the upper-level is not necessarily convex and the lower-level problem is strongly-convex, our proposed gradient-based $(\epsilon,\delta)$-DP algorithm returns a point with hypergradient norm at most $\widetilde{\mathcal{O}}\left((\sqrt{d_\mathrm{up}}/\epsilon n)^{1/2}+(\sqrt{d_\mathrm{low}}/\epsilon n)^{1/3}\right)$ where $n$ is the dataset size, and $d_\mathrm{up}/d_\mathrm{low}$ are the upper/lower level dimensions. Our analysis covers constrained and unconstrained problems alike, accounts for mini-batch gradients, and applies to both empirical and population losses. As an application, we specialize our analysis to derive a simple private rule for tuning a regularization hyperparameter.} }
Endnote
%0 Conference Paper %T Differentially Private Bilevel Optimization %A Guy Kornowski %B Proceedings of The 37th International Conference on Algorithmic Learning Theory %C Proceedings of Machine Learning Research %D 2026 %E Matus Telgarsky %E Jonathan Ullman %F pmlr-v313-kornowski26a %I PMLR %P 1--36 %U https://proceedings.mlr.press/v313/kornowski26a.html %V 313 %X We present differentially private (DP) algorithms for bilevel optimization, a problem class that received significant attention lately in various machine learning applications. These are the first algorithms for such problems under standard DP constraints, and are also the first to avoid Hessian computations which are prohibitive in large-scale settings. Under the well-studied setting in which the upper-level is not necessarily convex and the lower-level problem is strongly-convex, our proposed gradient-based $(\epsilon,\delta)$-DP algorithm returns a point with hypergradient norm at most $\widetilde{\mathcal{O}}\left((\sqrt{d_\mathrm{up}}/\epsilon n)^{1/2}+(\sqrt{d_\mathrm{low}}/\epsilon n)^{1/3}\right)$ where $n$ is the dataset size, and $d_\mathrm{up}/d_\mathrm{low}$ are the upper/lower level dimensions. Our analysis covers constrained and unconstrained problems alike, accounts for mini-batch gradients, and applies to both empirical and population losses. As an application, we specialize our analysis to derive a simple private rule for tuning a regularization hyperparameter.
APA
Kornowski, G.. (2026). Differentially Private Bilevel Optimization. Proceedings of The 37th International Conference on Algorithmic Learning Theory, in Proceedings of Machine Learning Research 313:1-36 Available from https://proceedings.mlr.press/v313/kornowski26a.html.

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