Feedback-Based Optimization with Sub-Weibull Gradient Errors and Intermittent Updates
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866911865580290048 |
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| author | Ospina, Ana M. Bastianello, Nicola Dall'Anese, Emiliano |
| author_facet | Ospina, Ana M. Bastianello, Nicola Dall'Anese, Emiliano |
| contents | This paper considers a feedback-based projected gradient method for optimizing systems modeled as algebraic maps. The focus is on a setup where the gradient is corrupted by random errors that follow a sub-Weibull distribution, and where the measurements of the output -- which replace the input-output map of the system in the algorithmic updates -- may not be available at each iteration. The sub-Weibull error model is particularly well-suited in frameworks where the cost of the problem is learned via Gaussian Process (GP) regression (from functional evaluations) concurrently with the execution of the algorithm; however, it also naturally models setups where nonparametric methods and neural networks are utilized to estimate the cost. Using the sub-Weibull model, and with Bernoulli random variables modeling missing measurements of the system output, we show that the online algorithm generates points that are within a bounded error from the optimal solutions. In particular, we provide error bounds in expectation and in high probability. Numerical results are presented in the context of a demand response problem in smart power grids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_06343 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Feedback-Based Optimization with Sub-Weibull Gradient Errors and Intermittent Updates Ospina, Ana M. Bastianello, Nicola Dall'Anese, Emiliano Optimization and Control Systems and Control This paper considers a feedback-based projected gradient method for optimizing systems modeled as algebraic maps. The focus is on a setup where the gradient is corrupted by random errors that follow a sub-Weibull distribution, and where the measurements of the output -- which replace the input-output map of the system in the algorithmic updates -- may not be available at each iteration. The sub-Weibull error model is particularly well-suited in frameworks where the cost of the problem is learned via Gaussian Process (GP) regression (from functional evaluations) concurrently with the execution of the algorithm; however, it also naturally models setups where nonparametric methods and neural networks are utilized to estimate the cost. Using the sub-Weibull model, and with Bernoulli random variables modeling missing measurements of the system output, we show that the online algorithm generates points that are within a bounded error from the optimal solutions. In particular, we provide error bounds in expectation and in high probability. Numerical results are presented in the context of a demand response problem in smart power grids. |
| title | Feedback-Based Optimization with Sub-Weibull Gradient Errors and Intermittent Updates |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2109.06343 |