The study of stable matchings usually relies on the assumption that agents' preferences over the opposite side are complete and known. In many real markets, however, preferences might be uncertain and revealed only through costly interactions such as interviews. We show how to reach interim-stable matchings, under which all matched pairs must have interviewed and agents use expected utilities whenever true values remain unknown, while minimizing both the expected number of interviews and the expected number of interview rounds. We introduce two adaptive algorithms that produce interim-stable matchings: one operates sequentially, and another is a hybrid algorithm that begins by scheduling some interviews in parallel and continues sequentially. Focusing on cases where agents are ex-ante indifferent between agents on the other side, we show that the sequential algorithm performs 2 interviews per agent in expectation. We complement this by showing that any algorithm that performs less than 2 interviews per agent, does not always guarantee interim-stability. We also demonstrate that the hybrid algorithm requires only polylogarithmic expected number of rounds, while still performing only about 2 interviews per agent in expectation. Additionally, the interviews scheduled by our algorithms guarantee an interim-stable matching when Deferred-Acceptance is run after all interviews are completed.

翻译：稳定匹配研究通常基于一个假设：参与者对另一侧参与者的偏好是完整且已知的。然而，在许多实际市场中，偏好可能具有不确定性，仅能通过面试等成本高昂的交互过程逐步揭示。本文探讨如何在实现临时稳定匹配的同时，最小化预期面试次数与预期面试轮次。在临时稳定匹配中，所有匹配对必须已完成面试，且参与者在真实价值未知时使用期望效用进行决策。我们提出了两种能生成临时稳定匹配的自适应算法：一种采用顺序执行模式，另一种为混合算法——初期并行安排部分面试，后续转为顺序执行。针对参与者对另一侧参与者存在事前无差异性的场景，我们证明顺序算法中每位参与者的预期面试次数为2次。我们进一步证明，任何使参与者平均面试次数低于2次的算法均无法始终保证临时稳定性。同时，我们验证了混合算法仅需多对数级别的预期轮次，且仍能保持每位参与者约2次的预期面试次数。此外，当所有面试完成后运行延迟接受算法时，本研究所提算法安排的面试能确保获得临时稳定匹配。