Sample Complexity of Chance Constrained Optimization in Dynamic Environment

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 in a sequential fashion 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.