Regret Minimization in Bilateral Trade With Perturbed Markets

TL;DR

This paper develops an adaptive algorithm for repeated buyer-seller trade that minimizes regret in markets with both stochastic and adversarial perturbations, bridging a key gap in trade efficiency.

Contribution

It introduces a novel algorithm that adaptively handles market perturbations, achieving near-optimal regret bounds in both stochastic and adversarial settings.

Findings

Achieves regret of O(T^{3/4}) + O(C log T) in perturbed markets.

Maintains worst-case O(T^{3/4}) regret in fully adversarial environments.

Bridges the gap between stochastic and adversarial market models.

Abstract

We address the problem of maximizing Gain from Trade (GFT) in repeated buyer-seller exchanges subject to global budget balance constraints. While this problem is well-understood in purely adversarial and stochastic settings, these environments exhibit a sharp dichotomy: adversarial environments allow for no-regret learning against the best fixed-price mechanism, whereas stochastic environments allow for no-regret learning against the best distribution over prices that is budget balanced in expectation. This gap is significant, as policies balanced in expectation can increase the GFT by a multiplicative factor of two. In this work, we bridge these extremes by studying perturbed markets, where an underlying stochastic distribution is subject to an adversarial corruption $C$. We design an algorithm that adaptively scales with the level of corruption, achieving an $\tilde{\mathcal{O}}(T^{3/4}) + \mathcal{O}(C\log(T))$ regret bound against the best budget-balanced distribution over prices. Simultaneously, our algorithm maintains the worst-case $\tilde{\mathcal{O}}(T^{3/4})$ regret bound relative to a per-round budget-balanced baseline, ensuring optimality even in fully adversarial environments.