Bilateral Trade Under Heavy-Tailed Valuations: Minimax Regret without a Variance Bound

תקציר מקורי באנגליתarXiv:2603.06851v4 Announce Type: replace-cross Abstract: In contextual bilateral trade under full feedback, the posted price does not affect which valuations are observed. We show that in this model such action-independent feedback removes the polynomial adaptation penalty familiar from heavy-tailed bandits: fully parameter-free algorithms attain the oracle minimax $T$-exponents up to logarithmic factors, with no knowledge of the moment order $p \in (1,2)$ or its scale $\sigma_p$, and -- in the nonparametric case -- none of the effective H\"older smoothness $\beta \in (0,1]$. The statistic that makes model selection possible is a paired squared-loss difference, whose noise-square term cancels exactly, leaving noise damped by the candidate gap. The resulting bilateral-trade regret rates ar