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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.10868 |
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| _version_ | 1866914553360547840 |
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| author | Castiglioni, Matteo Lunghi, Anna Marchesi, Alberto |
| author_facet | Castiglioni, Matteo Lunghi, Anna Marchesi, Alberto |
| contents | We study the sample complexity of learning a uniform approximation of an $n$-dimensional cumulative distribution function (CDF) within an error $ε> 0$, when observations are restricted to a minimal one-bit feedback. This serves as a counterpart to the multivariate DKW inequality under ''full feedback'', extending it to the setting of ''bandit feedback''. Our main result shows a near-dimensional-invariance in the sample complexity: we get a uniform $ε$-approximation with a sample complexity $\frac{1}{ε^3}{\log\left(\frac 1 ε\right)^{\mathcal{O}(n)}}$ over a arbitrary fine grid, where the dimensionality $n$ only affects logarithmic terms. As direct corollaries, we provide tight sample complexity bounds and novel regret guarantees for learning fixed-price mechanisms in small markets, such as bilateral trade settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10868 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Sample Complexity of Uniform Approximation for Multi-Dimensional CDFs and Fixed-Price Mechanisms Castiglioni, Matteo Lunghi, Anna Marchesi, Alberto Machine Learning We study the sample complexity of learning a uniform approximation of an $n$-dimensional cumulative distribution function (CDF) within an error $ε> 0$, when observations are restricted to a minimal one-bit feedback. This serves as a counterpart to the multivariate DKW inequality under ''full feedback'', extending it to the setting of ''bandit feedback''. Our main result shows a near-dimensional-invariance in the sample complexity: we get a uniform $ε$-approximation with a sample complexity $\frac{1}{ε^3}{\log\left(\frac 1 ε\right)^{\mathcal{O}(n)}}$ over a arbitrary fine grid, where the dimensionality $n$ only affects logarithmic terms. As direct corollaries, we provide tight sample complexity bounds and novel regret guarantees for learning fixed-price mechanisms in small markets, such as bilateral trade settings. |
| title | The Sample Complexity of Uniform Approximation for Multi-Dimensional CDFs and Fixed-Price Mechanisms |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2602.10868 |