Tight Regret Bounds for Bilateral Trade under Semi Feedback

TL;DR

This paper establishes tight regret bounds for fixed-price bilateral trade mechanisms under semi-feedback, providing a mechanism that matches the known lower bound up to polylogarithmic factors.

Contribution

It introduces a new mechanism achieving the optimal regret rate of rac{2}{3} in adversarial settings, resolving an open problem in the field.

Findings

Achieves rac{2}{3} regret bound matching the lower bound.

Provides a mechanism with near-optimal performance under semi-feedback.

Advances understanding of regret minimization in bilateral trade scenarios.

Abstract

The study of \textit{regret minimization in fixed-price bilateral trade} has received considerable attention in recent research. Previous works [CCC+24a, CCC+24b, AFF24, BCCF24, CJLZ25, LCM25a, GDFS25] have acquired a thorough understanding of the problem, except for determining the tight regret bound for GBB semi-feedback fixed-price mechanisms under adversarial values. In this paper, we resolve this open question by devising an $\widetilde{O}(T^{2 / 3})$-regret mechanism, matching the $\Omega(T^{2 / 3})$ lower bound from [CJLZ25] up to polylogarithmic factors.