Regret Minimization in Bilateral Trade With Perturbed Markets

2026-05-11

AI Summary

This study addresses bilateral trade under distributional perturbations, where the underlying stochastic distribution is subject to adversarial contamination, with the goal of maximizing gains from trade (GFT) under a global budget balance constraint. The work proposes a contamination-aware adaptive pricing algorithm that, for the first time in this setting, achieves no-regret learning with respect to the optimal budget-balanced price distribution. By integrating online learning with an adaptive adjustment mechanism, the algorithm dynamically balances performance across varying levels of contamination. Theoretical analysis shows that the algorithm attains a regret bound of Õ(T^{3/4}) + O(C log T) relative to the optimal distribution, and maintains a worst-case guarantee of Õ(T^{3/4}) even under fully adversarial conditions, thereby bridging the theoretical gap between purely stochastic and purely adversarial regimes.

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.

Problem

• Regret Minimization
• Bilateral Trade
• Budget Balance
• Perturbed Markets
• Gain from Trade

Innovation

• regret minimization
• bilateral trade
• perturbed markets
• budget balance
• adaptive learning