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<p>We study two-stage distributionally robust optimization (DRO) problems with decision-dependent information discovery (DDID) wherein (a portion of) the uncertain parameters are revealed only if an (often costly) investment is made at the first stage. This class of problems finds many important applications in selection problems (e.g., in hiring, project portfolio optimization, or optimal sensor location). Despite the wide applicability of the problem, it has not been previously studied. We propose a framework for modeling and approximately solving DRO problems with DDID. We formulate the problem as a min-max-min-max problem and adopt the popular&#xa0;<i>K</i>-adaptability approximation scheme, which chooses&#xa0;<i>K</i> candidate recourse actions here-and-now and implements the best of those actions after the uncertain parameters that were chosen to be observed are revealed. We then present a decomposition algorithm that solves the&#xa0;<i>K</i>-adaptable formulation exactly. In particular, we devise a cutting plane algorithm that iteratively solves a relaxed version of the problem, evaluates the true objective value of the corresponding solution, generates valid cuts, and imposes them on the relaxed problem. For the evaluation problem, we develop a branch-and-cut algorithm that provably converges to an optimal solution. We showcase the effectiveness of our framework on the R&amp;D project portfolio optimization problem and the best box problem.</p>

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Distributionally robust optimization with decision-dependent information discovery

  • 期刊论文

  • 发表日期：

    2026年4月20日

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  • Qing Jin,
  • Angelos Georghiou,
  • Phebe Vayanos,
  • Grani A. Hanasusanto

摘要

We study two-stage distributionally robust optimization (DRO) problems with decision-dependent information discovery (DDID) wherein (a portion of) the uncertain parameters are revealed only if an (often costly) investment is made at the first stage. This class of problems finds many important applications in selection problems (e.g., in hiring, project portfolio optimization, or optimal sensor location). Despite the wide applicability of the problem, it has not been previously studied. We propose a framework for modeling and approximately solving DRO problems with DDID. We formulate the problem as a min-max-min-max problem and adopt the popular K-adaptability approximation scheme, which chooses K candidate recourse actions here-and-now and implements the best of those actions after the uncertain parameters that were chosen to be observed are revealed. We then present a decomposition algorithm that solves the K-adaptable formulation exactly. In particular, we devise a cutting plane algorithm that iteratively solves a relaxed version of the problem, evaluates the true objective value of the corresponding solution, generates valid cuts, and imposes them on the relaxed problem. For the evaluation problem, we develop a branch-and-cut algorithm that provably converges to an optimal solution. We showcase the effectiveness of our framework on the R&D project portfolio optimization problem and the best box problem.