Better Regret Rates in Bilateral Trade via Sublinear Budget Violation

2025-07-15

AI Summary

This paper investigates the trade-off between budget balance constraints and regret rates in bilateral trade mechanism design. To overcome the limitation of strict global budget balance—which induces a high lower bound on regret—the authors propose a sublinear budget violation mechanism that permits controlled global budget deficits, bounded by at most $T^eta$. They establish, for the first time, the precise characterization of the trade-off between the budget violation exponent $eta$ and the achievable regret rate, thereby bridging a theoretical gap between local and global budget constraints. Their algorithm achieves an $ ilde{O}(T^{1 - eta/3})$ regret upper bound for $eta in [3/4, 6/7]$, and they prove this bound is tight. The approach integrates online learning with incentive-compatible mechanism design, employing rigorous upper- and lower-bound analyses to identify the optimal trade-off frontier.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Machine Learning: Online Learning & Bandits

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Bilateral trade is a central problem in algorithmic economics, and recent work has explored how to design trading mechanisms using no-regret learning algorithms. However, no-regret learning is impossible when budget balance has to be enforced at each time step. Bernasconi et al. [Ber+24] show how this impossibility can be circumvented by relaxing the budget balance constraint to hold only globally over all time steps. In particular, they design an algorithm achieving regret of the order of $ ilde O(T^{3/4})$ and provide a lower bound of $Ω(T^{5/7})$. In this work, we interpolate between these two extremes by studying how the optimal regret rate varies with the allowed violation of the global budget balance constraint. Specifically, we design an algorithm that, by violating the constraint by at most $T^β$ for any given $βin [frac{3}{4}, frac{6}{7}]$, attains regret $ ilde O(T^{1 - β/3})$. We complement this result with a matching lower bound, thus fully characterizing the trade-off between regret and budget violation. Our results show that both the $ ilde O(T^{3/4})$ upper bound in the global budget balance case and the $Ω(T^{5/7})$ lower bound under unconstrained budget balance violation obtained by Bernasconi et al. [Ber+24] are tight.

Problem

• Study regret rates in bilateral trade mechanisms
• Analyze trade-off between regret and budget violation
• Design algorithm with adjustable budget constraint violation

Innovation

• Sublinear budget violation for trade mechanisms
• Interpolates regret rates with budget constraints
• Matching lower bounds for trade-off analysis