mlsanityData to 14 Oct 2026

On the Inherent Privacy of Zeroth Order Projected Gradient Descent

arXiv 2507.05610 ↗First posted 8 Jul 2025math.OC cs.LG stat.MLcited by 0

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Abstract (arXiv)

Differentially private zeroth-order optimization methods have recently gained popularity in private fine tuning of machine learning models due to their reduced memory requirements. Current approaches for privatizing zeroth-order methods rely on adding Gaussian noise to the estimated zeroth-order gradients. However, since the search direction in the zeroth-order methods is inherently random, researchers including Tang et al. (2024) and Zhang et al. (2024a) have raised an important question: is the inherent noise in zeroth-order estimators sufficient to ensure the overall differential privacy of the algorithm? This work settles this question for a class of oracle-based optimization algorithms where the oracle returns zeroth-order gradient estimates. In particular, we show that for a fixed initialization, there exist strongly convex objective functions such that running (Projected) Zeroth-Order Gradient Descent (ZO-GD) is not differentially private. Furthermore, we show that even with random initialization and without revealing (initial and) intermediate iterates, the privacy loss in ZO-GD can grow superlinearly with the number of iterations when minimizing convex objective functions.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 34 of its 48 references that are in the map. First posted on arXiv 8 Jul 2025.

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34 of 48 references.

References · 34

  1. 2021LoRA: Low-Rank Adaptation of Large Language Modelscited by 14,380
  2. 2015Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classificationcited by 3,611
  3. 2016Deep Learning with Differential Privacycited by 2,728
  4. 2016Membership Inference Attacks against Machine Learning Modelscited by 2,281
  5. 2021Opacus: User-Friendly Differential Privacy Library in PyTorchcited by 383
  6. 2023Fine-Tuning Language Models with Just Forward Passescited by 345
  7. 2014RAPPOR: Randomized Aggregatable Privacy-Preserving Ordinal Responsecited by 272
  8. 2013Optimal rates for zero-order convex optimization: the power of two function evaluationscited by 198
  9. 2019Private Stochastic Convex Optimization with Optimal Ratescited by 186
  10. 2020Private Stochastic Convex Optimization: Optimal Rates in Linear Timecited by 153
  11. 2017Collecting Telemetry Data Privatelycited by 149
  12. 2024Revisiting Zeroth-Order Optimization for Memory-Efficient LLM Fine-Tuning: A Benchmarkcited by 114
22 more
  1. 2021Private Stochastic Convex Optimization: Optimal Rates in ℓ1 Geometrycited by 83
  2. 2021Differential Privacy Dynamics of Langevin Diffusion and Noisy Gradient Descentcited by 73
  3. 2022Privacy of Noisy Stochastic Gradient Descent: More Iterations without More Privacy Losscited by 61
  4. 2022Private Convex Optimization via Exponential Mechanismcited by 49
  5. 2024Private Fine-tuning of Large Language Models with Zeroth-order Optimizationcited by 41
  6. 2022Faster Rates of Convergence to Stationary Points in Differentially Private Optimizationcited by 32
  7. 2021Private Federated Learning Without a Trusted Server: Optimal Algorithms for Convex Lossescited by 30
  8. 2024Fine-Tuning Large Language Models with User-Level Differential Privacycited by 29
  9. 2024Zeroth-Order Fine-Tuning of LLMs with Extreme Sparsitycited by 28
  10. 2020LinkedIn's Audience Engagements API: A Privacy Preserving Data Analytics System at Scalecited by 26
  11. 2022Private Non-Convex Federated Learning Without a Trusted Servercited by 26
  12. 2023DPZero: Private Fine-Tuning of Language Models without Backpropagationcited by 26
  13. 2018Detecting Correlations with Little Memory and Communicationcited by 19
  14. 2022~Optimal Differentially Private Learning of Thresholds and Quasi-Concave Optimizationcited by 18
  15. 2023ReSQueing Parallel and Private Stochastic Convex Optimizationcited by 17
  16. 2022Private Convex Optimization in General Normscited by 13
  17. 2023Zeroth-order Optimization with Weak Dimension Dependencycited by 11
  18. 2019Private Learning Implies Online Learning: An Efficient Reductioncited by 10
  19. 2024How to Make the Gradients Small Privately: Improved Rates for Differentially Private Non-Convex Optimizationcited by 10
  20. 2024Private Zeroth-Order Nonsmooth Nonconvex Optimizationcited by 8
  21. 2024Private Heterogeneous Federated Learning Without a Trusted Server Revisited: Error-Optimal and Communication-Efficient Algorithms for Convex Lossescited by 8
  22. 2021Federated Learning with Heterogeneous Differential Privacycited by 5

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