AI and the World's Hard Problems · Theoretical computer science · arXiv · 2026-10-20
Variance Reduction for Stochastic Switching in Functionally Constrained Federated Optimization
In federated learning for safety-critical and fairness-sensitive applications, objectives must be optimized under functional constraints, which is challenging due to costly projection onto the feasible set, stochastic constraint information, partial client participation, and limited communication. The authors propose a federated stochastic switching framework based on primal-only updates that avoids dual-variable tuning, establishing high-probability convergence and feasibility guarantees under stochastic gradients and partial client participation. Variance-reducing constraint estimators yield vanishing feasibility and stationarity guarantees with fixed per-round client participation and constraint-evaluation batch sizes, and experiments on Neyman-Pearson classification, fairness-constrained learning on the ADULT dataset, and constrained deep reinforcement learning demonstrate the framework's effectiveness.