非参数上下文在线双边交易
Nonparametric Contextual Online Bilateral Trade
AI总结：
本文提出了一种非参数上下文在线双边交易算法，通过层次树构造在一位反馈和强预算平衡条件下实现~O(T^{(d-1)/d})的后悔界。
摘要：
我们研究了上下文在线双边交易的问题。在每一轮中，学习者面对一个卖方-买方对，并必须提出一个交易价格，而无需观察他们对所售物品的私人估值。学习者的目标是发布价格以促进双方之间的交易。在发布价格之前，学习者观察到一个d维的上下文向量，该向量影响代理的估值。先前在上下文设置中的工作主要集中在线性模型上。在本文中，我们针对一个一般性的非参数设置，其中买方和卖方的估值根据上下文的任意Lipschitz函数行为。我们设计了一个算法，通过层次树构造利用上下文信息，并保证了后悔为~O(T^{(d-1)/d})。值得注意的是，我们的算法在两个严格特征的设置下运行：(1) 一位反馈，即学习者只能观察到交易是否发生；(2) 强预算平衡，即学习者不能补贴或从市场参与者中获利。我们进一步在全反馈设置中提供了匹配的下界，证明了我们后悔界的一致性。
英文摘要：
We study the problem of contextual online bilateral trade. At each round, the learner faces a seller-buyer pair and must propose a trade price without observing their private valuations for the item being sold. The goal of the learner is to post prices to facilitate trades between the two parties. Before posting a price, the learner observes a $d$-dimensional context vector that influences the agent's valuations. Prior work in the contextual setting has focused on linear models. In this work, we tackle a general nonparametric setting in which the buyer's and seller's valuations behave according to arbitrary Lipschitz functions of the context. We design an algorithm that leverages contextual information through a hierarchical tree construction and guarantees regret $\widetilde{O}(T^{{(d-1)}/d})$. Remarkably, our algorithm operates under two stringent features of the setting: (1) one-bit feedback, where the learner only observes whether a trade occurred or not, and (2) strong budget balance, where the learner cannot subsidize or profit from the market participants. We further provide a matching lower bound in the full-feedback setting, demonstrating the tightness of our regret bound.
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