Constrained Optimization With Decision-Dependent Distributions

• 成果类型: Article
• 署名作者: Wang, Zifan; Liu, Changxin; Parisini, Thomas; Zavlanos, Michael M.; Johansson, Karl H.
• 署名单位: Royal Institute of Technology; East China University of Science & Technology; Imperial College London; Aalborg University; University of Trieste; Duke University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3540441
• 发表日期: 2025
• 页码: 5176-5189
• 关键词: Optimization; linear programming; CONVERGENCE; pricing; Machine learning algorithms; Heuristic algorithms; ELECTRONIC MAIL; training; Random variables; games; constrained optimization; decision-dependent distributions; dual ascent algorithms

摘要

In this article, we deal with stochastic optimization problems where the data distributions change in response to the decision variables. Traditionally, the study of optimization problems with decision-dependent distributions has assumed either the absence of constraints or fixed constraints. This work considers a more general setting where the constraints can also dynamically adjust in response to changes in the decision variables. Specifically, we consider linear constraints and analyze the effect of decision-dependent distributions in both the objective function and constraints. First, we establish a sufficient condition for the existence of a constrained equilibrium point, at which the distributions remain invariant under retraining. Moreover, we propose and analyze two algorithms: repeated constrained optimization and repeated dual ascent. For each algorithm, we provide sufficient conditions for convergence to the constrained equilibrium point. Furthermore, we explore the relationship between the equilibrium point and the optimal point for the constrained decision-dependent optimization problem. Notably, our results encompass previous findings as special cases when the constraints remain fixed. To show the effectiveness of our theoretical analysis, we provide numerical experiments on both a market problem and a dynamic pricing problem for parking based on real-world data.