# Private Non-Convex Federated Learning Without a Trusted Server

arXiv: https://arxiv.org/abs/2203.06735 · HTML: https://mlsanity.com/paper/2203.06735/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 59 of its 110 references that are in the map.
- First posted on arXiv 13 Mar 2022.

## Builds on (most cited first, 30 of 59)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [On the Convergence of FedAvg on Non-IID Data](https://mlsanity.com/paper/1907.02189/) (2019)
- [Deep Leakage from Gradients](https://mlsanity.com/paper/1906.08935/) (2019)
- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Condition](https://mlsanity.com/paper/1608.04636/) (2016)
- [Federated Learning with Differential Privacy: Algorithms and Performance Analysis](https://mlsanity.com/paper/1911.00222/) (2019)
- [Differentially Private Federated Learning: A Client Level Perspective](https://mlsanity.com/paper/1712.07557/) (2017)
- [A Unified Theory of Decentralized SGD with Changing Topology and Local Updates](https://mlsanity.com/paper/2003.10422/) (2020)
- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [Lower Bounds for Non-Convex Stochastic Optimization](https://mlsanity.com/paper/1912.02365/) (2019)
- [The Composition Theorem for Differential Privacy](https://mlsanity.com/paper/1311.0776/) (2013)
- [SPIDER: Near-Optimal Non-Convex Optimization via Stochastic Path Integrated Differential Estimator](https://mlsanity.com/paper/1807.01695/) (2018)
- [Federated Learning for Internet of Things: A Comprehensive Survey](https://mlsanity.com/paper/2104.07914/) (2021)
- [Loss landscapes and optimization in over-parameterized non-linear systems and neural networks](https://mlsanity.com/paper/2003.00307/) (2020)
- [A Hybrid Approach to Privacy-Preserving Federated Learning](https://mlsanity.com/paper/1812.03224/) (2018)
- [Private Stochastic Convex Optimization with Optimal Rates](https://mlsanity.com/paper/1908.09970/) (2019)
- [Amplification by Shuffling: From Local to Central Differential Privacy via Anonymity](https://mlsanity.com/paper/1811.12469/) (2018)
- [Private Stochastic Convex Optimization: Optimal Rates in Linear Time](https://mlsanity.com/paper/2005.04763/) (2020)
- [Is Local SGD Better than Minibatch SGD?](https://mlsanity.com/paper/2002.07839/) (2020)
- [Minibatch vs Local SGD for Heterogeneous Distributed Learning](https://mlsanity.com/paper/2006.04735/) (2020)
- [Concentrated Differential Privacy](https://mlsanity.com/paper/1603.01887/) (2016)
- [FedPD: A Federated Learning Framework with Optimal Rates and Adaptivity to Non-IID Data](https://mlsanity.com/paper/2005.11418/) (2020)
- [LDP-Fed: Federated Learning with Local Differential Privacy](https://mlsanity.com/paper/2006.03637/) (2020)
- [Differentially Private Empirical Risk Minimization Revisited: Faster and More General](https://mlsanity.com/paper/1802.05251/) (2018)
- [Distributed Differential Privacy via Shuffling](https://mlsanity.com/paper/1808.01394/) (2018)
- [Differentially Private Empirical Risk Minimization: Efficient Algorithms and Tight Error Bounds](https://mlsanity.com/paper/1405.7085/) (2014)
- [Hyperparameter Tuning with Renyi Differential Privacy](https://mlsanity.com/paper/2110.03620/) (2021)

## Built on by (most cited first, 26 of 26)

- [SoteriaFL: A Unified Framework for Private Federated Learning with Communication Compression](https://mlsanity.com/paper/2206.09888/) (2022)
- [On the Privacy-Robustness-Utility Trilemma in Distributed Learning](https://mlsanity.com/paper/2302.04787/) (2023)
- [Stochastic Differentially Private and Fair Learning](https://mlsanity.com/paper/2210.08781/) (2022)
- [On Differentially Private Federated Linear Contextual Bandits](https://mlsanity.com/paper/2302.13945/) (2023)
- [FedP3: Federated Personalized and Privacy-friendly Network Pruning under Model Heterogeneity](https://mlsanity.com/paper/2404.09816/) (2024)
- [How to Make the Gradients Small Privately: Improved Rates for Differentially Private Non-Convex Optimization](https://mlsanity.com/paper/2402.11173/) (2024)
- [Optimal Differentially Private Model Training with Public Data](https://mlsanity.com/paper/2306.15056/) (2023)
- [ULDP-FL: Federated Learning with Across Silo User-Level Differential Privacy](https://mlsanity.com/paper/2308.12210/) (2023)
- [Cross-silo Federated Learning with Record-level Personalized Differential Privacy](https://mlsanity.com/paper/2401.16251/) (2024)
- [Private Heterogeneous Federated Learning Without a Trusted Server Revisited: Error-Optimal and Communication-Efficient Algorithms for Convex Losses](https://mlsanity.com/paper/2407.09690/) (2024)
- [Differentially Private Non-Convex Optimization under the KL Condition with Optimal Rates](https://mlsanity.com/paper/2311.13447/) (2023)
- [Toward the Tradeoffs between Privacy, Fairness and Utility in Federated Learning](https://mlsanity.com/paper/2311.18190/) (2023)
- [PrivSGP-VR: Differentially Private Variance-Reduced Stochastic Gradient Push with Tight Utility Bounds](https://mlsanity.com/paper/2405.02638/) (2024)
- [Private Stochastic Optimization With Large Worst-Case Lipschitz Parameter](https://mlsanity.com/paper/2209.07403/) (2022)
- [Private and Federated Stochastic Convex Optimization: Efficient Strategies for Centralized Systems](https://mlsanity.com/paper/2407.12396/) (2024)
- [Smoothed Normalization for Efficient Distributed Private Optimization](https://mlsanity.com/paper/2502.13482/) (2025)
- [Second-Order Convergence in Private Stochastic Non-Convex Optimization](https://mlsanity.com/paper/2505.15647/) (2025)
- [Research in Collaborative Learning Does Not Serve Cross-Silo Federated Learning in Practice](https://mlsanity.com/paper/2510.12595/) (2025)
- [Privacy-Preserving Federated Convex Optimization: Balancing Partial-Participation and Efficiency via Noise Cancellation](https://mlsanity.com/paper/2506.02563/) (2025)
- [DP-CSGP: Differentially Private Stochastic Gradient Push with Compressed Communication](https://mlsanity.com/paper/2512.13583/) (2025)
- [First Provable Guarantees for Practical Private FL: Beyond Restrictive Assumptions](https://mlsanity.com/paper/2512.21521/) (2025)
- [ERIS: Enhancing the Privacy-Utility-Scalability Trade-Off in Federated Learning via Federated Shard Aggregation](https://mlsanity.com/paper/2602.08617/) (2026)
- [Convergent Differential Privacy Analysis for General Federated Learning](https://mlsanity.com/paper/2408.15621/) (2024)
- [A Stochastic Optimization Framework for Private and Fair Learning From Decentralized Data](https://mlsanity.com/paper/2411.07889/) (2024)
- [Personalized Federated Training of Diffusion Models with Privacy Guarantees](https://mlsanity.com/paper/2504.00952/) (2025)
- [On the Inherent Privacy of Zeroth Order Projected Gradient Descent](https://mlsanity.com/paper/2507.05610/) (2025)

## Abstract (arXiv)

We study federated learning (FL) -- especially cross-silo FL -- with non-convex loss functions and data from people who do not trust the server or other silos. In this setting, each silo (e.g. hospital) must protect the privacy of each person's data (e.g. patient's medical record), even if the server or other silos act as adversarial eavesdroppers. To that end, we consider inter-silo record-level (ISRL) differential privacy (DP), which requires silo~i's communications to satisfy record/item-level DP. We propose novel ISRL-DP algorithms for FL with heterogeneous (non-i.i.d.) silo data and two classes of Lipschitz continuous loss functions: First, we consider losses satisfying the Proximal Polyak-Lojasiewicz (PL) inequality, which is an extension of the classical PL condition to the constrained setting. In contrast to our result, prior works only considered unconstrained private optimization with Lipschitz PL loss, which rules out most interesting PL losses such as strongly convex problems and linear/logistic regression. Our algorithms nearly attain the optimal strongly convex, homogeneous (i.i.d.) rate for ISRL-DP FL without assuming convexity or i.i.d. data. Second, we give the first private algorithms for non-convex non-smooth loss functions. Our utility bounds even improve on the state-of-the-art bounds for smooth losses. We complement our upper bounds with lower bounds. Additionally, we provide shuffle DP (SDP) algorithms that improve over the state-of-the-art central DP algorithms under more practical trust assumptions. Numerical experiments show that our algorithm has better accuracy than baselines for most privacy levels. All the codes are publicly available at: https://github.com/ghafeleb/Private-NonConvex-Federated-Learning-Without-a-Trusted-Server.