Nonparametric Contextual Online Bilateral Trade

TL;DR

This paper introduces a nonparametric approach to online bilateral trade with contextual information, achieving near-optimal regret bounds under minimal feedback and budget constraints.

Contribution

It develops a hierarchical tree-based algorithm for nonparametric contextual trade, extending beyond linear models, with proven regret bounds and matching lower bounds.

Findings

Regret bound of O(T^{(d-1)/d}) for the proposed algorithm

Algorithm operates effectively with one-bit feedback and no market subsidies

Matching lower bound established in the full-feedback setting

Abstract

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.