Heterogeneity within data distribution poses a challenge in many modern federated learning tasks. We formalize it as an optimization problem involving a computationally heavy composite under data similarity. By employing different sets of assumptions, we present several approaches to develop communication-efficient methods. An optimal algorithm is proposed for the convex case. The constructed theory is validated through a series of experiments across various problems.
@article{arxiv.2601.08614,
title = {Accelerated Methods with Complexity Separation Under Data Similarity for Federated Learning Problems},
author = {Dmitry Bylinkin and Sergey Skorik and Dmitriy Bystrov and Leonid Berezin and Aram Avetisyan and Aleksandr Beznosikov},
journal= {arXiv preprint arXiv:2601.08614},
year = {2026}
}