Distributed Constrained Online Nonconvex Optimization with Compressed Communication
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911128854986752 |
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| author | Zhang, Kunpeng Xu, Lei Yi, Xinlei Cao, Ming Johansson, Karl H. Chai, Tianyou Yang, Tao |
| author_facet | Zhang, Kunpeng Xu, Lei Yi, Xinlei Cao, Ming Johansson, Karl H. Chai, Tianyou Yang, Tao |
| contents | This paper considers distributed online nonconvex optimization with time-varying inequality constraints over a network of agents. For a time-varying graph, we propose a distributed online primal-dual algorithm with compressed communication to efficiently utilize communication resources. We show that the proposed algorithm establishes an $\mathcal{O}( {{T^{\max \{ {1 - {θ_1},{θ_1}} \}}}} )$ network regret bound and an $\mathcal{O}( {T^{1 - {θ_1}/2}} )$ network cumulative constraint violation bound, where $T$ is the number of iterations and ${θ_1} \in ( {0,1} )$ is a user-defined trade-off parameter. When Slater's condition holds (i.e, there is a point that strictly satisfies the inequality constraints at all iterations), the network cumulative constraint violation bound is reduced to $\mathcal{O}( {T^{1 - {θ_1}}} )$. These bounds are comparable to the state-of-the-art results established by existing distributed online algorithms with perfect communication for distributed online convex optimization with (time-varying) inequality constraints. Finally, a simulation example is presented to validate the theoretical results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_22410 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distributed Constrained Online Nonconvex Optimization with Compressed Communication Zhang, Kunpeng Xu, Lei Yi, Xinlei Cao, Ming Johansson, Karl H. Chai, Tianyou Yang, Tao Optimization and Control Systems and Control This paper considers distributed online nonconvex optimization with time-varying inequality constraints over a network of agents. For a time-varying graph, we propose a distributed online primal-dual algorithm with compressed communication to efficiently utilize communication resources. We show that the proposed algorithm establishes an $\mathcal{O}( {{T^{\max \{ {1 - {θ_1},{θ_1}} \}}}} )$ network regret bound and an $\mathcal{O}( {T^{1 - {θ_1}/2}} )$ network cumulative constraint violation bound, where $T$ is the number of iterations and ${θ_1} \in ( {0,1} )$ is a user-defined trade-off parameter. When Slater's condition holds (i.e, there is a point that strictly satisfies the inequality constraints at all iterations), the network cumulative constraint violation bound is reduced to $\mathcal{O}( {T^{1 - {θ_1}}} )$. These bounds are comparable to the state-of-the-art results established by existing distributed online algorithms with perfect communication for distributed online convex optimization with (time-varying) inequality constraints. Finally, a simulation example is presented to validate the theoretical results. |
| title | Distributed Constrained Online Nonconvex Optimization with Compressed Communication |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2503.22410 |