To address efficiency and design challenges in choice-based matching platforms, we introduce a two-sided assortment optimization framework under general choice preferences. The goal in this problem is to maximize the expected number of matches by deciding which assortments are displayed to the agents and the order in which they are shown. In this context, we identify several classes of policies that platforms can use in their design. Our goals are: (1) to measure the value that one class of policies has over another one, and (2) to approximately solve the optimization problem itself for a given class. For (1), we define the adaptivity gap as the worst-case ratio between the optimal values of two different policy classes. First, we show that the gap between the class of policies that statically show assortments to one-side first and the class of policies that adaptively show assortments to one-side first is exactly $e/(e-1)$. Second, we show that the gap between the latter class of policies and the fully adaptive class of policies that show assortments to agents one by one is exactly $2$. We also note that the worst policies are those who simultaneously show assortments to all the agents. For (2), we first design a polynomial time algorithm that achieves a $1/4$ approximation factor within the class of policies that adaptively show assortments to agents one by one. Furthermore, when agents' preferences are governed by multinomial-logit models, we show that a 0.067 approximation factor can be obtained within the class of policies that show assortments to all agents at once. We further generalize our results to constrained assortment settings, where we impose an upper bound on the size of the displayed assortments. Finally, we present a computational study to evaluate the empirical performance of our theoretical guarantees.

翻译：针对基于选择的匹配平台中的效率与设计挑战，我们提出了一种在广义选择偏好下的双面组合优化框架。该问题的目标是通过决定向智能体展示哪些组合及其展示顺序来最大化期望匹配数量。在此背景下，我们识别了平台在设计过程中可采用的几类策略。我们的目标是：（1）量化某一类策略相对于另一类策略的价值，以及（2）针对特定策略类别近似求解该优化问题本身。对于目标（1），我们将适应性差距定义为两类不同策略最优值之间的最坏情况比率。首先，我们证明静态优先向一侧展示组合的策略类别与自适应优先向一侧展示组合的策略类别之间的差距恰为$e/(e-1)$。其次，我们证明后一类策略与逐个向智能体自适应展示组合的完全自适应策略类别之间的差距恰为$2$。同时注意到，最差的策略是同时向所有智能体展示组合的策略。对于目标（2），我们首先设计了一个多项式时间算法，在逐个向智能体自适应展示组合的策略类别中实现了$1/4$的近似因子。此外，当智能体的偏好服从多项式逻辑模型时，我们证明在同时向所有智能体展示组合的策略类别中可获得0.067的近似因子。我们进一步将结果推广至约束组合场景，即对展示组合的规模设置上限。最后，我们通过计算实验评估了理论保证的实证表现。