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arXiv · 2404.00608

Sample Complexity of Chance Constrained Optimization in Dynamic Environment

Apurv Shukla·Qian Zhang·Le Xie
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Abstract

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.

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Apurv Shukla, Qian Zhang, Le Xie. 2024-03-31. Sample Complexity of Chance Constrained Optimization in Dynamic Environment. https://arxiv.org/abs/2404.00608

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