# Dimension Independent Generalization of DP-SGD for Overparameterized Smooth Convex Optimization

arXiv: https://arxiv.org/abs/2206.01836 · HTML: https://mlsanity.com/paper/2206.01836/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 15 references that are in the map.
- First posted on arXiv 3 Jun 2022.

## Builds on (most cited first, 9 of 9)

- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Renyi Differential Privacy](https://mlsanity.com/paper/1702.07476/) (2017)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [Privacy Amplification by Subsampling: Tight Analyses via Couplings and Divergences](https://mlsanity.com/paper/1807.01647/) (2018)
- [Private Stochastic Convex Optimization with Optimal Rates](https://mlsanity.com/paper/1908.09970/) (2019)
- [Stability of Stochastic Gradient Descent on Nonsmooth Convex Losses](https://mlsanity.com/paper/2006.06914/) (2020)
- [Private Stochastic Convex Optimization: Optimal Rates in Linear Time](https://mlsanity.com/paper/2005.04763/) (2020)
- [Differentially Private Empirical Risk Minimization: Efficient Algorithms and Tight Error Bounds](https://mlsanity.com/paper/1405.7085/) (2014)
- [When is the Convergence Time of Langevin Algorithms Dimension Independent? A Composite Optimization Viewpoint](https://mlsanity.com/paper/2110.01827/) (2021)

## Built on by (most cited first, 9 of 9)

- [Exploring the Limits of Differentially Private Deep Learning with Group-wise Clipping](https://mlsanity.com/paper/2212.01539/) (2022)
- [When Does Differentially Private Learning Not Suffer in High Dimensions?](https://mlsanity.com/paper/2207.00160/) (2022)
- [DPZero: Private Fine-Tuning of Language Models without Backpropagation](https://mlsanity.com/paper/2310.09639/) (2023)
- [Pre-training Differentially Private Models with Limited Public Data](https://mlsanity.com/paper/2402.18752/) (2024)
- [Lower Generalization Bounds for GD and SGD in Smooth Stochastic Convex Optimization](https://mlsanity.com/paper/2303.10758/) (2023)
- [Differentially Private Optimization with Sparse Gradients](https://mlsanity.com/paper/2404.10881/) (2024)
- [A Theoretical Survey on Foundation Models](https://mlsanity.com/paper/2410.11444/) (2024)
- [Stabilization of Perturbed Loss Function: Differential Privacy without Gradient Noise](https://mlsanity.com/paper/2508.15523/) (2025)
- [Generalization Bounds of Stochastic Gradient Descent in Homogeneous Neural Networks](https://mlsanity.com/paper/2602.22936/) (2026)

## Abstract (arXiv)

This paper considers the generalization performance of differentially private convex learning. We demonstrate that the convergence analysis of Langevin algorithms can be used to obtain new generalization bounds with differential privacy guarantees for DP-SGD. More specifically, by using some recently obtained dimension-independent convergence results for stochastic Langevin algorithms with convex objective functions, we obtain O(n-1/4) privacy guarantees for DP-SGD with the optimal excess generalization error of tildeO(n-1/2) for certain classes of overparameterized smooth convex optimization problems. This improves previous DP-SGD results for such problems that contain explicit dimension dependencies, so that the resulting generalization bounds become unsuitable for overparameterized models used in practical applications.