We advance a recently flourishing line of work at the intersection of learning theory and computational economics by studying the learnability of two classes of mechanisms prominent in economics, namely menus of lotteries and two-part tariffs. The former is a family of randomized mechanisms designed for selling multiple items, known to achieve revenue beyond deterministic mechanisms, while the latter is designed for selling multiple units (copies) of a single item with applications in real-world scenarios such as car or bike-sharing services. We focus on learning high-revenue mechanisms of this form from buyer valuation data in both distributional settings, where we have access to buyers' valuation samples up-front, and the more challenging and less-studied online settings, where buyers arrive one-at-a-time and no distributional assumption is made about their values. Our main contribution is proposing the first online learning algorithms for menus of lotteries and two-part tariffs with strong regret-bound guarantees. In the general case, we provide a reduction to a finite number of experts, and in the limited buyer type case, we show a reduction to online linear optimization, which allows us to obtain no-regret guarantees by presenting buyers with menus that correspond to a barycentric spanner. In addition, we provide algorithms with improved running times over prior work for the distributional settings. The key difficulty when deriving learning algorithms for these settings is that the relevant revenue functions have sharp transition boundaries. In stark contrast with the recent literature on learning such unstructured functions, we show that simple discretization-based techniques are sufficient for learning in these settings.

翻译：我们推进了学习理论与计算经济学交叉领域近期蓬勃发展的研究方向，通过研究两类经济学经典机制的可学习性：彩票菜单机制与二部定价机制。前者是为多物品销售设计的随机化机制族，已被证明能实现超越确定性机制的收益；后者则针对单物品多单位（副本）销售场景设计，在汽车或共享单车等现实服务中具有广泛应用。我们聚焦于从买家估值数据中学习此类高收益机制，涵盖两种典型场景：分布式场景中可预先获取买家估值样本，以及更具挑战性且研究较少的在线场景——买家逐一到达且其估值不依赖任何分布假设。本文的主要贡献在于首次提出针对彩票菜单与二部定价机制的在线学习算法，并给出强后悔界保证。在一般情形下，我们通过归约至有限专家集实现学习；在有限买家类型情形中，则通过归约至在线线性优化，通过向买家呈现对应重心跨度的菜单以获得无后悔保证。此外，我们针对分布式场景提出较先前工作运行时间更优的算法。推导这些场景学习算法的核心难点在于相关收益函数存在尖锐的转换边界。与近期关于此类非结构化函数学习的研究截然不同，我们证明简单的基于离散化的技术足以实现这些场景下的有效学习。