Bilateral Trade Under Heavy-Tailed Valuations: Minimax Regret with Infinite Variance

arXiv:2603.06851v2 Announce Type: replace Abstract: We study contextual bilateral trade under full feedback when, conditionally on the context, trader valuations have bounded density but infinite variance. We first extend the self-bounding property of Bachoc et al. (ICML 2025) from bounded to real-valued valuations, showing that the expected regret of any price pi satisfies a quadratic self-bounding inequality under bounded density alone. Combining this with truncated-mean estimation, we prove that an epoch-based algorithm achieves regret O~(T^{1 - 2beta(p-1)/(betap + d(p-1))}) when the noise has finite p-th moment for p in (1,2) and the market value function is beta-Holder, and we establish a matching lower bound via Assouad's method with a fixed-support mixture construction. Our results characterize the exact minimax rate in T for this problem, interpolating between the classical nonparametric rate at p=2 and the trivial linear rate as p tends to 1.