In our work, we propose the first distributed method with client sampling and provable tolerance to Byzantine workers.

Biased gradient compression with error feedback (EF) reduces communication in federated learning (FL), but under non-IID data, the residual error can decay slowly, causing gradient mismatch and stalled progress in the early rounds. We propose step-ahead partial error feedback (SA-PEF), which integrates step-ahead (SA) correction with partial error feedback (PEF). SA-PEF recovers EF when the step-ahead coefficient α = 0 and step-ahead EF (SAEF) when α = 1. For non-convex objectives and δ-contractive compressors, we establish a second-moment bound and a residual recursion that guarantee convergence to stationar-ity under heterogeneous data and partial client participation. To balance SAEF's rapid warm-up with EF's long-term stability, we select α near its theory-predicted optimum. Experiments across diverse architectures and datasets show that SA-PEF consistently reaches target accuracy faster than EF. Modern large-scale machine learning increasingly relies on distributed computation, where both data and compute are spread across many devices. Federated learning (FL) enables model training in this setting without centralizing raw data, enhancing privacy and scalability under heterogeneous client distributions (McMahan et al., 2017; Kairouz et al., 2021). In each synchronous FL round, the server broadcasts the current global model to a subset of clients. These clients perform several steps of stochastic gradient descent (SGD) on their local data and return updates to the server, which aggregates them to form the next global iterate (Huang et al., 2022; Wang & Ji, 2022; Li et al., 2024). Although FL leverages rich distributed data, it faces two key challenges.

We introduce FedSGM, a unified framework for federated constrained optimization that addresses four major challenges in federated learning (FL): functional constraints, communication bottlenecks, local updates, and partial client participation. Building on the switching gradient method, FedSGM provides projection-free, primal-only updates, avoiding expensive dual-variable tuning or inner solvers. To handle communication limits, FedSGM incorporates bi-directional error feedback, correcting the bias introduced by compression while explicitly understanding the interaction between compression noise and multi-step local updates. We derive convergence guarantees showing that the averaged iterate achieves the canonical $\boldsymbol{\mathcal{O}}(1/\sqrt{T})$ rate, with additional high-probability bounds that decouple optimization progress from sampling noise due to partial participation. Additionally, we introduce a soft switching version of FedSGM to stabilize updates near the feasibility boundary. To our knowledge, FedSGM is the first framework to unify functional constraints, compression, multiple local updates, and partial client participation, establishing a theoretically grounded foundation for constrained federated learning. Finally, we validate the theoretical guarantees of FedSGM via experimentation on Neyman-Pearson classification and constrained Markov decision process (CMDP) tasks.

We present a new method that includes three key components of distributed optimization and federated learning: variance reduction of stochastic gradients, partial participation, and compressed communication. We prove that the new method has optimal oracle complexity and state-of-the-art communication complexity in the partial participation setting. Regardless of the communication compression feature, our method successfully combines variance reduction and partial participation: we get the optimal oracle complexity, never need the participation of all nodes, and do not require the bounded gradients (dissimilarity) assumption.

Satellite constellations in low-Earth orbit are now widespread, enabling positioning, Earth imaging, and communications. In this paper we address the solution of learning problems using these satellite constellations. In particular, we focus on a federated approach, where satellites collect and locally process data, with the ground station aggregating local models. We focus on designing a novel, communication-efficient algorithm that still yields accurate trained models. To this end, we employ several mechanisms to reduce the number of communications with the ground station (local training) and their size (compression). We then propose an error feedback mechanism that enhances accuracy, which yields, as a byproduct, an algorithm-agnostic error feedback scheme that can be more broadly applied. We analyze the convergence of the resulting algorithm, and compare it with the state of the art through simulations in a realistic space scenario, showcasing superior performance.

R is a smooth nonconvex function for all j [ m]. We assume that Assumptions 1, 2 and 3 hold and the following assumption.

R is a smooth nonconvex function for all j [ m]. We assume that Assumptions 1, 2 and 3 hold and the following assumption.

However, FL is usually computationally intensive.