# One-Shot Federated Learning: Theoretical Limits and Algorithms to Achieve Them

arXiv: https://arxiv.org/abs/1905.04634 · HTML: https://mlsanity.com/paper/1905.04634/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 May 2019.

## Built on by (most cited first, 23 of 23)

- [FedDM: Iterative Distribution Matching for Communication-Efficient Federated Learning](https://mlsanity.com/paper/2207.09653/) (2022)
- [One-Shot Federated Conformal Prediction](https://mlsanity.com/paper/2302.06322/) (2023)
- [One-shot Federated Learning without Server-side Training](https://mlsanity.com/paper/2204.12493/) (2022)
- [Non-IID Quantum Federated Learning with One-shot Communication Complexity](https://mlsanity.com/paper/2209.00768/) (2022)
- [FLIX: A Simple and Communication-Efficient Alternative to Local Methods in Federated Learning](https://mlsanity.com/paper/2111.11556/) (2021)
- [Federated Few-Shot Learning with Adversarial Learning](https://mlsanity.com/paper/2104.00365/) (2021)
- [One-Shot Federated Learning for LEO Constellations that Reduces Convergence Time from Days to 90 Minutes](https://mlsanity.com/paper/2305.12316/) (2023)
- [Navigating Heterogeneity and Privacy in One-Shot Federated Learning with Diffusion Models](https://mlsanity.com/paper/2405.01494/) (2024)
- [A One-shot Framework for Distributed Clustered Learning in Heterogeneous Environments](https://mlsanity.com/paper/2209.10866/) (2022)
- [CPS Attack Detection under Limited Local Information in Cyber Security: A Multi-node Multi-class Classification Ensemble Approach](https://mlsanity.com/paper/2209.00170/) (2022)
- [Towards One-shot Federated Learning: Advances, Challenges, and Future Directions](https://mlsanity.com/paper/2505.02426/) (2025)
- [Efficient Federated Learning with Heterogeneous Data and Adaptive Dropout](https://mlsanity.com/paper/2507.10430/) (2025)
- [Harnessing Federated Generative Learning for Green and Sustainable Internet of Things](https://mlsanity.com/paper/2407.05915/) (2024)
- [FedMHO: Heterogeneous One-Shot Federated Learning Towards Resource-Constrained Edge Devices](https://mlsanity.com/paper/2502.08518/) (2025)
- [One-Shot Federated Ridge Regression: Exact Recovery via Sufficient Statistic Aggregation](https://mlsanity.com/paper/2601.08216/) (2026)
- [Order Optimal Bounds for One-Shot Federated Learning over non-Convex Loss Functions](https://mlsanity.com/paper/2108.08677/) (2021)
- [HEX: Human-in-the-loop Explainability via Deep Reinforcement Learning](https://mlsanity.com/paper/2206.01343/) (2022)
- [FedPNN: One-shot Federated Classification via Evolving Clustering Method and Probabilistic Neural Network hybrid](https://mlsanity.com/paper/2304.04147/) (2023)
- [Federated Classification in Hyperbolic Spaces via Secure Aggregation of Convex Hulls](https://mlsanity.com/paper/2308.06895/) (2023)
- [Distributed Continual Learning with CoCoA in High-dimensional Linear Regression](https://mlsanity.com/paper/2312.01795/) (2023)
- [Enhancing Federated Learning with Adaptive Differential Privacy and Priority-Based Aggregation](https://mlsanity.com/paper/2406.18491/) (2024)
- [CRIP: Channel Level Representation Injection for Personalized One-Shot Federated Learning](https://mlsanity.com/paper/2608.02222/) (2026)
- [Structural Entropy-Driven Graph Diffusion Generation for One-Shot Federated Graph Learning](https://mlsanity.com/paper/2609.06499/) (2026)

## Abstract (arXiv)

We consider distributed statistical optimization in one-shot setting, where there are m machines each observing n i.i.d. samples. Based on its observed samples, each machine sends a B-bit-long message to a server. The server then collects messages from all machines, and estimates a parameter that minimizes an expected convex loss function. We investigate the impact of communication constraint, B, on the expected error and derive a tight lower bound on the error achievable by any algorithm. We then propose an estimator, which we call Multi-Resolution Estimator (MRE), whose expected error (when B≥log mn) meets the aforementioned lower bound up to poly-logarithmic factors, and is thereby order optimal. We also address the problem of learning under tiny communication budget, and present lower and upper error bounds when B is a constant. The expected error of MRE, unlike existing algorithms, tends to zero as the number of machines (m) goes to infinity, even when the number of samples per machine (n) remains upper bounded by a constant. This property of the MRE algorithm makes it applicable in new machine learning paradigms where m is much larger than n.