Robust Optimization with Decision-Dependent Information Discovery

作者：Phebe Vayanos, Angelos Georghiou, Yubing Han · 发表于：Management Science · 年份：2025 · DOI：10.1287/mnsc.2021.00160 · 被引用次数：25 · 研究领域：Risk and Portfolio Optimization、Multi-Criteria Decision Making、Fuzzy Systems and Optimization

Robust optimization (RO) is a popular paradigm for modeling and solving two- and multistage decision-making problems affected by uncertainty. In many real-world applications, such as R&D project selection, production planning, or preference elicitation for product or policy recommendations, the time of information discovery is decision-dependent and the uncertain parameters only become observable after an often costly investment. Yet, most of the literature on robust optimization assumes that the uncertain parameters can be observed for free and that the sequence in which they are revealed is independent of the decision-maker’s actions. To fill this gap in the practicability of RO, we consider two- and multistage robust optimization problems in which part of the decision variables control the time of information discovery. Thus, information available at any given time is decision-dependent and can be discovered (at least in part) by making strategic exploratory investments in previous stages. We propose a novel dynamic formulation of the problem and prove its correctness. We leverage our model to provide a solution method inspired from the K-adaptability approximation, whereby K candidate strategies for each decision stage are chosen here-and-now and, at the beginning of each period, the best of these strategies is selected after the uncertain parameters that were chosen to be observed are revealed. We reformulate the problem as a finite mixed-integer (resp. bilinear) pro...