Pandora's problem is a fundamental model in economics that studies optimal search strategies under costly inspection. In this paper we initiate the study of Pandora's problem with combinatorial costs, capturing many real-life scenarios where search cost is non-additive. Weitzman's celebrated algorithm [1979] establishes the remarkable result that, for additive costs, the optimal search strategy is non-adaptive and computationally feasible. We inquire to which extent this structural and computational simplicity extends beyond additive cost functions. Our main result is that the class of submodular cost functions admits an optimal strategy that follows a fixed, non-adaptive order, thus preserving the structural simplicity of additive cost functions. In contrast, for the more general class of subadditive (or even XOS) cost functions, the optimal strategy may already need to determine the search order adaptively. On the computational side, obtaining any approximation to the optimal utility requires super polynomially many queries to the cost function, even for a strict subclass of submodular cost functions.

翻译：潘多拉问题是一个经济学中的基本模型，用于研究在成本高昂的检查条件下的最优搜索策略。本文首次研究了带有组合成本的潘多拉问题，其中搜索成本是非可加性的，这捕捉到了许多现实场景。Weitzman著名的算法[1979]揭示了这样一个显著结果：对于可加性成本，最优搜索策略是非适应性的且计算上可行。我们探究这种结构与计算上的简洁性在多大程度上能扩展到可加成本函数之外。我们的主要结果是：子模成本函数类别允许存在一条遵循固定非适应性顺序的最优策略，从而保留了可加成本函数的结构简洁性。相比之下，对于更一般的子可加（甚至XOS）成本函数，最优策略可能已经需要自适应地确定搜索顺序。在计算方面，即使是针对子模成本函数的一个严格子类，要获得最优效用的任何近似，也需要对成本函数进行超多项式次查询。