论文标题
在线收入最大化与未知凹面公用事业
Online Revenue Maximization with Unknown Concave Utilities
论文作者
论文摘要
我们研究了一个在线收入最大化问题，消费者从一些未知的分销中到达I.I.D，并从卖家那里购买了一堆产品。经典方法通常会完全了解消费者效用功能，而最近的作品专门用于未知的线性实用程序功能。鉴于它们是凹的，本文着重于具有未知消费者分销和未知消费者公用事业的在线发布价格模型。因此，要问的两个问题是我）卖方的在线最大化问题是什么，ii）如何找到非线性实用程序的最佳定价策略。我们通过对实用程序施加三阶平滑度条件来回答第一个问题。第二个问题是由两种算法解决的，我们证明这是$ o（t^{\ frac {2} {3}}} {\ log t）^{\ frac {\ frac {1} {1} {3}} {3}} {3}}）$（ t）^{\ frac {1} {2}}）$。
We study an online revenue maximization problem where the consumers arrive i.i.d from some unknown distribution and purchase a bundle of products from the sellers. The classical approach generally assumes complete knowledge of the consumer utility functions, while recent works have been devoted to unknown linear utility functions. This paper focuses on the online posted-price model with unknown consumer distribution and unknown consumer utilities, given they are concave. Hence, the two questions to ask are i) when is the seller's online maximization problem concave, and ii) how to find the optimal pricing strategy for non-linear utilities. We answer the first question by imposing a third-order smoothness condition on the utilities. The second question is addressed by two algorithms, which we prove to exhibit the sub-linear regrets of $O(T^{\frac{2}{3}} (\log T)^{\frac{1}{3}})$ and $O(T^{\frac{1}{2}} (\log T)^{\frac{1}{2}})$ respectively.
