# Stochastic Adaptive Line Search for Differentially Private Optimization

arXiv: https://arxiv.org/abs/2008.07978 · HTML: https://mlsanity.com/paper/2008.07978/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Aug 2020.

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

- [Deep Learning with Label Differential Privacy](https://mlsanity.com/paper/2102.06062/) (2021)
- [Not all noise is accounted equally: How differentially private learning benefits from large sampling rates](https://mlsanity.com/paper/2110.06255/) (2021)
- [DPIS: An Enhanced Mechanism for Differentially Private SGD with Importance Sampling](https://mlsanity.com/paper/2210.09634/) (2022)
- [Efficient Hyperparameter Optimization for Differentially Private Deep Learning](https://mlsanity.com/paper/2108.03888/) (2021)
- [Differentially Private Optimization for Smooth Nonconvex ERM](https://mlsanity.com/paper/2302.04972/) (2023)
- [Learning Privacy-Preserving Student Networks via Discriminative-Generative Distillation](https://mlsanity.com/paper/2409.02404/) (2024)
- [DP-SGD with weight clipping](https://mlsanity.com/paper/2310.18001/) (2023)
- [AdvSGM: Differentially Private Graph Learning via Adversarial Skip-gram Model](https://mlsanity.com/paper/2503.21426/) (2025)
- [Structure-Preference Enabled Graph Embedding Generation under Differential Privacy](https://mlsanity.com/paper/2501.03451/) (2025)

## Abstract (arXiv)

The performance of private gradient-based optimization algorithms is highly dependent on the choice of step size (or learning rate) which often requires non-trivial amount of tuning. In this paper, we introduce a stochastic variant of classic backtracking line search algorithm that satisfies R'enyi differential privacy. Specifically, the proposed algorithm adaptively chooses the step size satsisfying the the Armijo condition (with high probability) using noisy gradients and function estimates. Furthermore, to improve the probability with which the chosen step size satisfies the condition, it adjusts per-iteration privacy budget during runtime according to the reliability of noisy gradient. A naive implementation of the backtracking search algorithm may end up using unacceptably large privacy budget as the ability of adaptive step size selection comes at the cost of extra function evaluations. The proposed algorithm avoids this problem by using the sparse vector technique combined with the recent privacy amplification lemma. We also introduce a privacy budget adaptation strategy in which the algorithm adaptively increases the budget when it detects that directions pointed by consecutive gradients are drastically different. Extensive experiments on both convex and non-convex problems show that the adaptively chosen step sizes allow the proposed algorithm to efficiently use the privacy budget and show competitive performance against existing private optimizers.