Safe-EF: Error Feedback for Nonsmooth Constrained Optimization (2505.06053v1)

Abstract: 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.

Safe-EF: Error Feedback for Nonsmooth Constrained Optimization

The paper "Safe-EF: Error Feedback for Nonsmooth Constrained Optimization" explores the field of distributed optimization, with a particular emphasis on federated learning scenarios. This paradigm, especially in privacy-sensitive and resource-constrained environments, introduces notable communication challenges due to the high dimensionality of model updates. The primary focus of this paper is the development and empirical analysis of the Safe-EF algorithm, a variant of Error Feedback (EF), which seeks to address these challenges in non-smooth constrained optimization settings.

Key Contributions

The authors present several fundamental contributions within this paper:

1. Lower Complexity Bounds: They establish new lower complexity bounds for first-order algorithms employing contractive compression, specifically within the non-smooth convex setting. These bounds are crucial as they provide benchmarks against which the efficacy of new algorithms can be measured.
2. Safe-EF Algorithm: A core contribution is the introduction of the Safe-EF algorithm, which matches the new lower complexity bound up to a constant. Notably, Safe-EF enforces safety constraints that are critical for practical applications. This ensures that solutions adhere to feasibility requirements, which is particularly important in safety-critical applications.
3. Stochastic Extension: Safe-EF's applicability is extended to stochastic settings. This extension is pivotal given real-world scenarios often involve stochastic data inputs rather than deterministic queries. The paper provides high probability bounds on the algorithm's performance, enhancing its practical utility.
4. Experimental Validation: Extensive experimental tests showcase the proficiency of Safe-EF in a reinforcement learning setup. These experiments simulate distributed humanoid robot training, highlighting Safe-EF's ability to maintain safety and reduce communication complexity.

Numerical Results and Insights

The paper highlights several key numerical results. In particular, they illustrate how Safe-EF achieves a balanced trade-off between communication efficiency and solution optimality. Through distributed humanoid training, Safe-EF demonstrates reduced communication overhead while maintaining constraint satisfaction, thus validating its practical effectiveness in federated settings. The algorithm's ability to work with Top-$K$ compressors further underscores its adaptability in real-world applications.

Comparison with Prior Work

The work notably contrasts with previous EF-based algorithms, which were predominantly tailored for smooth, unconstrained optimization problems. The paper provides illustrative examples where both CGD and EF21 fail on non-smooth problems, highlighting the robustness of Safe-EF under these challenging conditions.

Additionally, the Safe-EF algorithm addresses practical constraints by dynamically adjusting its optimization strategy based on constraint violations—a feature not present in traditional EF methods. As such, Safe-EF expands the applicability of EF methods to constrained scenarios that are common in federated reinforcement learning and beyond.

Future Directions

The authors briefly touch upon future work avenues by noting several limitations within the current framework. Some promising directions include exploring non-convex optimization scenarios, relaxing noise assumptions, and enhancing the sample efficiency of Safe-EF in stochastic settings. Moreover, potential improvements in the dependency on compression levels represent another frontier for exploration.

Conclusion

The paper presents significant advancements in the field of federated learning and distributed optimization. By addressing both non-smooth objective functions and safety constraints, Safe-EF emerges as a promising solution, as validated by theoretical insight and empirical evidence. The work signifies a step forward in making federated learning more communication-efficient, especially in real-world applications where safety cannot be compromised.