$\ell_{\infty}$ Vector Contraction for Rademacher Complexity

Dylan J. Foster; Alexander Rakhlin

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arXiv · 1911.06468

$\ell_{\infty}$ Vector Contraction for Rademacher Complexity

Dylan J. Foster·Alexander Rakhlin

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Abstract

We show that the Rademacher complexity of any $\mathbb{R}^{K}$-valued function class composed with an $\ell_{\infty}$-Lipschitz function is bounded by the maximum Rademacher complexity of the restriction of the function class along each coordinate, times a factor of $\tilde{O}(\sqrt{K})$.

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Dylan J. Foster, Alexander Rakhlin. 2019-11-15. $\ell_{\infty}$ Vector Contraction for Rademacher Complexity. https://arxiv.org/abs/1911.06468

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