{"ID":2867648,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.17659","arxiv_id":"2509.17659","title":"Distributed Stochastic Optimization under Heavy-Tailed Noise: A Federated Mirror Descent Approach with High Probability Convergence","abstract":"We study the distributed stochastic optimization (DSO) problem under a heavy-tailed noise condition by utilizing a multi-agent system. Despite the extensive research on DSO algorithms used to solve DSO problems under light-tailed noise conditions (such as Gaussian noise), there is a significant lack of study of DSO algorithms in the context of heavy-tailed random noise. Classical DSO approaches in a heavy-tailed setting may present poor convergence behaviors. Therefore, developing DSO methods in the context of heavy-tailed noises is of importance. This work follows this path and we consider the setting that the gradient noises associated with each agent can be heavy-tailed, potentially having unbounded variance. We propose a clipped federated stochastic mirror descent algorithm to solve the DSO problem. We rigorously present a convergence theory and show that, under appropriate rules on the stepsize and the clipping parameter associated with the local noisy gradient influenced by the heavy-tailed noise, the algorithm is able to achieve satisfactory high probability convergence.","short_abstract":"We study the distributed stochastic optimization (DSO) problem under a heavy-tailed noise condition by utilizing a multi-agent system. Despite the extensive research on DSO algorithms used to solve DSO problems under light-tailed noise conditions (such as Gaussian noise), there is a significant lack of study of DSO alg...","url_abs":"https://arxiv.org/abs/2509.17659","url_pdf":"https://arxiv.org/pdf/2509.17659v1","authors":"[\"Zhan Yu\",\"Lan Liao\",\"Deming Yuan\",\"Daniel W. C. Ho\",\"Ding-Xuan Zhou\"]","published":"2025-09-22T12:03:19Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}