We study learnability of two important classes of mechanisms, menus of lotteries and two-part tariffs. A menu of lotteries is a list of entries where each entry is a pair consisting of probabilities of allocating each item and a price. Menus of lotteries is an especially important family of randomized mechanisms that are known to achieve revenue beyond any deterministic mechanism. A menu of two-part tariffs, on the other hand, is a pricing scheme (that consists of an up-front fee and a per unit fee) that is commonly used in the real world, e.g., for car or bike sharing services. We study learning high-revenue menus of lotteries and two-part tariffs from buyer valuation data in both distributional settings, where we have access to buyers' valuation samples up-front, and 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. Furthermore, 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：我们研究了两类重要机制——抽奖菜单和两部定价机制——的可学习性。抽奖菜单是一组条目列表，每个条目由分配各物品的概率与价格组成。作为随机化机制中特别重要的一类，抽奖菜单已被证明能够实现超越任何确定性机制的收入。另一方面，两部定价菜单是一种定价方案（包含预付费和单位使用费），在现实世界中广泛使用，例如汽车或自行车共享服务。我们研究从买家估值数据中学习高收益的抽奖菜单和两部定价机制，涵盖两种场景：分布设定场景中可预先获取买家估值样本，以及在线设定场景中买家逐个到达且不假设其估值分布。我们的主要贡献是首次提出具有强遗憾界保证的抽奖菜单和两部定价在线学习算法。此外，我们还提供了相比先前工作在分布设定下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过渡边界。与近期关于学习此类非结构化函数的文献形成鲜明对比，我们证明了基于简单离散化的技术已足以在这些场景中实现有效学习。