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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2603.06851 |
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| _version_ | 1866915842044723200 |
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| author | Zhao, Hangyi |
| author_facet | Zhao, Hangyi |
| contents | We study contextual bilateral trade under full feedback when 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 $π$ satisfies $\mathbb{E}[g(m,V,W) - g(π,V,W)] \le L|m-π|^2$ under bounded density alone. Combining this with truncated-mean estimation, we prove that an epoch-based algorithm achieves regret $\widetilde{O}(T^{1-2β(p-1)/(βp + d(p-1))})$ when the noise has finite $p$-th moment for $p \in (1,2)$ and the market value function is $β$-Hölder, and we establish a matching $Ω(\cdot)$ lower bound via Assouad's method with a smoothed moment-matching construction. Our results characterize the exact minimax rate for this problem, interpolating between the classical nonparametric rate at $p=2$ and the trivial linear rate as $p \to 1^+$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_06851 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bilateral Trade Under Heavy-Tailed Valuations: Minimax Regret with Infinite Variance Zhao, Hangyi Machine Learning Computer Science and Game Theory We study contextual bilateral trade under full feedback when 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 $π$ satisfies $\mathbb{E}[g(m,V,W) - g(π,V,W)] \le L|m-π|^2$ under bounded density alone. Combining this with truncated-mean estimation, we prove that an epoch-based algorithm achieves regret $\widetilde{O}(T^{1-2β(p-1)/(βp + d(p-1))})$ when the noise has finite $p$-th moment for $p \in (1,2)$ and the market value function is $β$-Hölder, and we establish a matching $Ω(\cdot)$ lower bound via Assouad's method with a smoothed moment-matching construction. Our results characterize the exact minimax rate for this problem, interpolating between the classical nonparametric rate at $p=2$ and the trivial linear rate as $p \to 1^+$. |
| title | Bilateral Trade Under Heavy-Tailed Valuations: Minimax Regret with Infinite Variance |
| topic | Machine Learning Computer Science and Game Theory |
| url | https://arxiv.org/abs/2603.06851 |