# Sample Optimality and All-for-all Strategies in Personalized Federated and Collaborative Learning

arXiv: https://arxiv.org/abs/2201.13097 · HTML: https://mlsanity.com/paper/2201.13097/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2022.

## Built on by (most cited first, 3 of 3)

- [Refined Convergence and Topology Learning for Decentralized SGD with Heterogeneous Data](https://mlsanity.com/paper/2204.04452/) (2022)
- [Decentralized Personalized Federated Learning](https://mlsanity.com/paper/2406.06520/) (2024)
- [Personalized Collaborative Learning with Affinity-Based Variance Reduction](https://mlsanity.com/paper/2510.16232/) (2025)

## Abstract (arXiv)

In personalized Federated Learning, each member of a potentially large set of agents aims to train a model minimizing its loss function averaged over its local data distribution. We study this problem under the lens of stochastic optimization. Specifically, we introduce information-theoretic lower bounds on the number of samples required from all agents to approximately minimize the generalization error of a fixed agent. We then provide strategies matching these lower bounds, in the all-for-one and all-for-all settings where respectively one or all agents desire to minimize their own local function. Our strategies are based on a gradient filtering approach: provided prior knowledge on some notions of distances or discrepancies between local data distributions or functions, a given agent filters and aggregates stochastic gradients received from other agents, in order to achieve an optimal bias-variance trade-off.