Feedback-Based Optimization with Sub-Weibull Gradient Errors and Intermittent Updates
| Autor: | Ospina, Ana M., Bastianello, Nicola, Dall'Anese, Emiliano |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1109/LCSYS.2022.3167947 |
| Popis: | 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. Comment: Version of the IEEE Control Systems Letters (L-CSS) paper with one typo corrected |
| Databáze: | arXiv |
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