{"ID":2845376,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.04456","arxiv_id":"2511.04456","title":"Federated Stochastic Minimax Optimization under Heavy-Tailed Noises","abstract":"Heavy-tailed noise has attracted growing attention in nonconvex stochastic optimization, as numerous empirical studies suggest it offers a more realistic assumption than standard bounded variance assumption. In this work, we investigate nonconvex-PL minimax optimization under heavy-tailed gradient noise in federated learning. We propose two novel algorithms: Fed-NSGDA-M, which integrates normalized gradients, and FedMuon-DA, which leverages the Muon optimizer for local updates. Both algorithms are designed to effectively address heavy-tailed noise in federated minimax optimization, under a milder condition. We theoretically establish that both algorithms achieve a convergence rate of $O({1}/{(TNp)^{\\frac{s-1}{2s}}})$. To the best of our knowledge, these are the first federated minimax optimization algorithms with rigorous theoretical guarantees under heavy-tailed noise. Extensive experiments further validate their effectiveness.","short_abstract":"Heavy-tailed noise has attracted growing attention in nonconvex stochastic optimization, as numerous empirical studies suggest it offers a more realistic assumption than standard bounded variance assumption. In this work, we investigate nonconvex-PL minimax optimization under heavy-tailed gradient noise in federated le...","url_abs":"https://arxiv.org/abs/2511.04456","url_pdf":"https://arxiv.org/pdf/2511.04456v1","authors":"[\"Xinwen Zhang\",\"Hongchang Gao\"]","published":"2025-11-06T15:27:29Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false}