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. We provide a suite of results with regard to these two families of mechanisms. We provide the first online learning algorithms for menus of lotteries and two-part tariffs with strong regret-bound guarantees. Since the space of parameters is infinite and the revenue functions have discontinuities, the known techniques do not readily apply. However, we are able to provide a reduction to online learning over a finite number of experts, in our case, a finite number of parameters. Furthermore, in the limited buyers 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. Finally, we demonstrate how techniques from the recent literature in data-driven algorithm design are insufficient for our studied problems.

翻译：本研究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，通过探究经济学中两类重要机制——彩票菜单与两部定价制——的可学习性。前者是为销售多物品设计的随机机制族，已知其收益能力超越确定性机制；后者则为销售单一物品的多个单位（副本）而设计，在汽车共享或自行车共享等现实场景中具有应用价值。我们专注于从买家估值数据中学习此类形式的高收益机制，研究涵盖两种设定：分布式设定（可预先获取买家估值样本）与更具挑战性且研究较少的在线设定（买家逐一到达且对其估值不作分布假设）。针对这两类机制，我们提供了一系列研究成果。我们首次提出了具有强遗憾界保证的彩票菜单与两部定价制在线学习算法。由于参数空间无限且收益函数存在间断性，现有技术无法直接适用。然而，我们成功实现了向有限专家数（即有限参数集）在线学习的归约。此外，在有限买家类型情形下，我们展示了向在线线性优化的归约，通过向买家呈现对应于重心生成元的菜单，从而获得无悔保证。同时，我们提出了在分布式设定下运行时间优于已有工作的改进算法。最后，我们论证了近期数据驱动算法设计文献中的技术对于本研究问题存在不足。