We study the design of multi-item mechanisms that maximize expected profit
with respect to a distribution over buyers' values. In practice, a full
description of the distribution is typically unavailable. Therefore, we study
the setting where the designer only has samples from the distribution and the
goal is to find a high-profit mechanism within a class of mechanisms. If the
class is complex, a mechanism may have high average profit over the samples but
low expected profit. This raises the question: how many samples are sufficient
to ensure that a mechanism's average profit is close to its expected profit? To
answer this question, we uncover structure shared by many pricing, auction, and
lottery mechanisms: for any set of buyers' values, profit is piecewise linear
in the mechanism's parameters. Using this structure, we prove new bounds for
mechanism classes not yet studied in the sample-based mechanism design
literature and match or improve over the best known guarantees for many
classes. Finally, we provide tools for optimizing an important tradeoff: more
complex mechanisms typically have higher average profit over the samples than
simpler mechanisms, but more samples are required to ensure that average profit
nearly matches expected profit.

本文探讨基于样本分布设计多项货品机制，利用分段线性结构证明了利润上限，并提出了优化复杂性和准确性之间的平衡的工具。

多商品利润最大化的泛化保证：定价、拍卖和随机机制

Generalization Guarantees for Multi-item Profit Maximization: Pricing,  Auctions, and Randomized Mechanisms

Traditional recommendation systems make recommendations based solely on the
customer's past purchases, product ratings and demographic data without
considering the profitability the items being recommended. In this work we
study the question of how a vendor can directly incorporate the profitability
of items into its recommender so as to maximize its expected profit while still
providing accurate recommendations. Our approach uses the output of any
traditional recommender system and adjust them according to item
profitabilities. Our approach is parameterized so the vendor can control how
much the recommendation incorporating profits can deviate from the traditional
recommendation. We study our approach under two settings and show that it
achieves approximately 22% more profit than traditional recommendations.

本研究研究了如何将商品盈利纳入推荐系统，以最大化销售利润，同时提供准确的推荐建议，方法是将传统推荐算法的结果根据商品盈利性进行调整，并通过设置参数控制建议和传统算法结果的差距程度。研究结果表明该方法比传统模型提高了约 22% 的利润。