{"ID":2882573,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.09411","arxiv_id":"2508.09411","title":"Distributed Online Stochastic Convex-Concave Optimization: Dynamic Regret Analyses under Single and Multiple Consensus Steps","abstract":"This paper considers the distributed online convex-concave optimization with constraint sets over a multiagent network, in which each agent autonomously generates a series of decision pairs through a designable mechanism to cooperatively minimize the global loss function. To this end, under no-Euclidean distance metrics, we propose a distributed online stochastic mirror descent convex-concave optimization algorithm with time-varying predictive mappings. Taking dynamic saddle point regret as a performance metric, it is proved that the proposed algorithm achieves the regret upper-bound in $\\mathcal{O}(\\max \\{T^{θ_1}, T^{θ_2} (1+V_T ) \\})$ for the general convex-concave loss function, where $θ_1, θ_2 \\in(0,1)$ are the tuning parameters, $T$ is the total iteration time, and $V_T$ is the path-variation. Surely, this algorithm guarantees the sublinear convergence, provided that $V_T$ is sublinear. Moreover, aiming to achieve better convergence, we further investigate a variant of this algorithm by employing the multiple consensus technique. The obtained results show that the appropriate setting can effectively tighten the regret bound to a certain extent. Finally, the efficacy of the proposed algorithms is validated and compared through the simulation example of a target tracking problem.","short_abstract":"This paper considers the distributed online convex-concave optimization with constraint sets over a multiagent network, in which each agent autonomously generates a series of decision pairs through a designable mechanism to cooperatively minimize the global loss function. To this end, under no-Euclidean distance metric...","url_abs":"https://arxiv.org/abs/2508.09411","url_pdf":"https://arxiv.org/pdf/2508.09411v1","authors":"[\"Wentao Zhang\",\"Baoyong Zhang\",\"Deming Yuan\",\"Shengyuan Xu\",\"Vincent K. N. Lau\"]","published":"2025-08-13T01:03:08Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}