Distributed and Inexact Proximal Gradient Method for Online Convex Optimization
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2020
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| _version_ | 1866909188746117120 |
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| author | Bastianello, Nicola Dall'Anese, Emiliano |
| author_facet | Bastianello, Nicola Dall'Anese, Emiliano |
| contents | This paper develops and analyzes an online distributed proximal-gradient method (DPGM) for time-varying composite convex optimization problems. Each node of the network features a local cost that includes a smooth strongly convex function and a non-smooth convex function, both changing over time. By coordinating through a connected communication network, the nodes collaboratively track the trajectory of the minimizers without exchanging their local cost functions. The DPGM is implemented in an online fashion, that is, in a setting where only a limited number of steps are implemented before the function changes. Moreover, the algorithm is analyzed in an inexact scenario, that is, with a source of additive noise, that can represent e.g. communication noise or quantization. It is shown that the tracking error of the online inexact DPGM is upper-bounded by a convergent linear system, guaranteeing convergence within a neighborhood of the optimal solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_00870 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Distributed and Inexact Proximal Gradient Method for Online Convex Optimization Bastianello, Nicola Dall'Anese, Emiliano Optimization and Control This paper develops and analyzes an online distributed proximal-gradient method (DPGM) for time-varying composite convex optimization problems. Each node of the network features a local cost that includes a smooth strongly convex function and a non-smooth convex function, both changing over time. By coordinating through a connected communication network, the nodes collaboratively track the trajectory of the minimizers without exchanging their local cost functions. The DPGM is implemented in an online fashion, that is, in a setting where only a limited number of steps are implemented before the function changes. Moreover, the algorithm is analyzed in an inexact scenario, that is, with a source of additive noise, that can represent e.g. communication noise or quantization. It is shown that the tracking error of the online inexact DPGM is upper-bounded by a convergent linear system, guaranteeing convergence within a neighborhood of the optimal solution. |
| title | Distributed and Inexact Proximal Gradient Method for Online Convex Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2001.00870 |