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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2508.09411 |
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| _version_ | 1866913987813179392 |
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| author | Zhang, Wentao Zhang, Baoyong Yuan, Deming Xu, Shengyuan Lau, Vincent K. N. |
| author_facet | Zhang, Wentao Zhang, Baoyong Yuan, Deming Xu, Shengyuan Lau, Vincent K. N. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09411 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distributed Online Stochastic Convex-Concave Optimization: Dynamic Regret Analyses under Single and Multiple Consensus Steps Zhang, Wentao Zhang, Baoyong Yuan, Deming Xu, Shengyuan Lau, Vincent K. N. Optimization and Control 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. |
| title | Distributed Online Stochastic Convex-Concave Optimization: Dynamic Regret Analyses under Single and Multiple Consensus Steps |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2508.09411 |