The Ledoux-Talagrand contraction inequality states $\mathfrak{R}_n(\varphi \circ \mathcal{F}) \leq \kappa L \cdot \mathfrak{R}_n(\mathcal{F})$ for $L$-Lipschitz $\varphi$ with $\varphi(0) = 0$. What is the canonical constant $\kappa$ in the standard (non-symmetric) statement?

Contraction Inequality

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120sadvanced (7/10)state theorem

The Ledoux-Talagrand contraction inequality states R_{n} (φ \circ F) \leq κ L \cdot R_{n} (F) for L -Lipschitz φ with φ (0) = 0 . What is the canonical constant κ in the standard (non-symmetric) statement?