Sample Complexity of Chance Constrained Optimization in Dynamic Environment
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914736337059840 |
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| author | Shukla, Apurv Zhang, Qian Xie, Le |
| author_facet | Shukla, Apurv Zhang, Qian Xie, Le |
| contents | We study the scenario approach for solving chance-constrained optimization in time-coupled dynamic environments. Scenario generation methods approximate the true feasible region from scenarios generated independently and identically from the actual distribution. In this paper, we consider this problem in a dynamic environment, where the scenarios are assumed to be drawn sequentially from an unknown and time-varying distribution. Such dynamic environments are driven by changing environmental conditions that could be found in many real-world applications such as energy systems. We couple the time-varying distributions using the Wasserstein metric between the sequence of scenario-generating distributions and the actual chance-constrained distribution. Our main results are bounds on the number of samples essential for ensuring the ex-post risk in chance-constrained optimization problems when the underlying feasible set is convex or non-convex. Finally, our results are illustrated on multiple numerical experiments for both types of feasible sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00608 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sample Complexity of Chance Constrained Optimization in Dynamic Environment Shukla, Apurv Zhang, Qian Xie, Le Optimization and Control Systems and Control We study the scenario approach for solving chance-constrained optimization in time-coupled dynamic environments. Scenario generation methods approximate the true feasible region from scenarios generated independently and identically from the actual distribution. In this paper, we consider this problem in a dynamic environment, where the scenarios are assumed to be drawn sequentially from an unknown and time-varying distribution. Such dynamic environments are driven by changing environmental conditions that could be found in many real-world applications such as energy systems. We couple the time-varying distributions using the Wasserstein metric between the sequence of scenario-generating distributions and the actual chance-constrained distribution. Our main results are bounds on the number of samples essential for ensuring the ex-post risk in chance-constrained optimization problems when the underlying feasible set is convex or non-convex. Finally, our results are illustrated on multiple numerical experiments for both types of feasible sets. |
| title | Sample Complexity of Chance Constrained Optimization in Dynamic Environment |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2404.00608 |