First-Order Softmax Weighted Switching Gradient Method for Distributed Stochastic Minimax Optimization with Stochastic Constraints

• URL: http://arxiv.org/abs/2603.05774v1
• Date: Fri, 06 Mar 2026 00:14:46 GMT
• Title: First-Order Softmax Weighted Switching Gradient Method for Distributed Stochastic Minimax Optimization with Stochastic Constraints
• Abstract summary: We propose a novel first-order Softmax-Weighted Switching Gradient method tailored for federated learning.<n>Under full client participation, our algorithm achieves the standard $mathcalO(-4)$ oracle complexity.<n>We provide a unified error decomposition and establish a sharp $mathcalO(logfrac1)$ high-probability convergence guarantee.
• Score: 9.141425189503794
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper addresses the distributed stochastic minimax optimization problem subject to stochastic constraints. We propose a novel first-order Softmax-Weighted Switching Gradient method tailored for federated learning. Under full client participation, our algorithm achieves the standard $\mathcal{O}(ε^{-4})$ oracle complexity to satisfy a unified bound $ε$ for both the optimality gap and feasibility tolerance. We extend our theoretical analysis to the practical partial participation regime by quantifying client sampling noise through a stochastic superiority assumption. Furthermore, by relaxing standard boundedness assumptions on the objective functions, we establish a strictly tighter lower bound for the softmax hyperparameter. We provide a unified error decomposition and establish a sharp $\mathcal{O}(\log\frac{1}δ)$ high-probability convergence guarantee. Ultimately, our framework demonstrates that a single-loop primal-only switching mechanism provides a stable alternative for optimizing worst-case client performance, effectively bypassing the hyperparameter sensitivity and convergence oscillations often encountered in traditional primal-dual or penalty-based approaches. We verify the efficacy of our algorithm via experiment on the Neyman-Pearson (NP) classification and fair classification tasks.

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