# Safe-EF: Error Feedback for Nonsmooth Constrained Optimization

arXiv: https://arxiv.org/abs/2505.06053 · HTML: https://mlsanity.com/paper/2505.06053/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 May 2025.

## Built on by (most cited first, 6 of 6)

- [Composite Optimization with Error Feedback: the Dual Averaging Approach](https://mlsanity.com/paper/2510.03507/) (2025)
- [First-Order Softmax Weighted Switching Gradient Method for Distributed Stochastic Minimax Optimization with Stochastic Constraints](https://mlsanity.com/paper/2603.05774/) (2026)
- [Byzantine-Robust and Differentially Private Federated Optimization under Weaker Assumptions](https://mlsanity.com/paper/2603.23472/) (2026)
- [Distributed Online Convex Optimization with Compressed Communication: Optimal Regret and Applications](https://mlsanity.com/paper/2604.09276/) (2026)
- [SA-PEF: Step-Ahead Partial Error Feedback for Efficient Federated Learning](https://mlsanity.com/paper/2601.20738/) (2026)
- [Global Optimality for Constrained Exploration via Penalty Regularization](https://mlsanity.com/paper/2604.28144/) (2026)

## Abstract (arXiv)

Federated learning faces severe communication bottlenecks due to the high dimensionality of model updates. Communication compression with contractive compressors (e.g., Top-K) is often preferable in practice but can degrade performance without proper handling. Error feedback (EF) mitigates such issues but has been largely restricted for smooth, unconstrained problems, limiting its real-world applicability where non-smooth objectives and safety constraints are critical. We advance our understanding of EF in the canonical non-smooth convex setting by establishing new lower complexity bounds for first-order algorithms with contractive compression. Next, we propose Safe-EF, a novel algorithm that matches our lower bound (up to a constant) while enforcing safety constraints essential for practical applications. Extending our approach to the stochastic setting, we bridge the gap between theory and practical implementation. Extensive experiments in a reinforcement learning setup, simulating distributed humanoid robot training, validate the effectiveness of Safe-EF in ensuring safety and reducing communication complexity.