Online Convex Optimization Using Coordinate Descent Algorithms
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866914769054728192 |
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| author | Lin, Yankai Shames, Iman Nešić, Dragan |
| author_facet | Lin, Yankai Shames, Iman Nešić, Dragan |
| contents | This paper considers the problem of online optimization where the objective function is time-varying. In particular, we extend coordinate descent type algorithms to the online case, where the objective function varies after a finite number of iterations of the algorithm. Instead of solving the problem exactly at each time step, we only apply a finite number of iterations at each time step. Commonly used notions of regret are used to measure the performance of the online algorithm. Moreover, coordinate descent algorithms with different updating rules are considered, including both deterministic and stochastic rules that are developed in the literature of classical offline optimization. A thorough regret analysis is given for each case. Finally, numerical simulations are provided to illustrate the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_10017 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Online Convex Optimization Using Coordinate Descent Algorithms Lin, Yankai Shames, Iman Nešić, Dragan Optimization and Control Systems and Control 68Q32 (Primary), 68T05, 90C25 (Secondary) This paper considers the problem of online optimization where the objective function is time-varying. In particular, we extend coordinate descent type algorithms to the online case, where the objective function varies after a finite number of iterations of the algorithm. Instead of solving the problem exactly at each time step, we only apply a finite number of iterations at each time step. Commonly used notions of regret are used to measure the performance of the online algorithm. Moreover, coordinate descent algorithms with different updating rules are considered, including both deterministic and stochastic rules that are developed in the literature of classical offline optimization. A thorough regret analysis is given for each case. Finally, numerical simulations are provided to illustrate the theoretical results. |
| title | Online Convex Optimization Using Coordinate Descent Algorithms |
| topic | Optimization and Control Systems and Control 68Q32 (Primary), 68T05, 90C25 (Secondary) |
| url | https://arxiv.org/abs/2201.10017 |