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Ecole Nationale de la Statistique et de l'Administration Economique

Academic institutioneurope · fr
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Representative Papers

Kernel Methods for Refined Prophet Inequalities

Aug 09, 2026

This work addresses the performance degradation of the classical single-threshold strategy in single-choice prophet inequalities under ill-behaved distributions by introducing a relative variance constraint on the maximum as a nonparametric complexity measure. It pioneers the application of kernel methods to this domain, constructing a linear functional optimization framework over quantile function spaces. By establishing a strong minimax duality and leveraging infinite-dimensional convex programming alongside variational analysis, the paper precisely characterizes the optimal threshold under bounded variance conditions. Key contributions include an exact performance curve under the i.i.d. setting, an asymptotically optimal threshold for finite horizons, closed-form solutions for non-i.i.d. cases, and a rigorous separation of the performance bounds between the prophet-secretary model and the i.i.d. benchmark.

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Latest Papers

Kernel Methods for Refined Prophet Inequalities

Aug 09, 2026

This work addresses the performance degradation of the classical single-threshold strategy in single-choice prophet inequalities under ill-behaved distributions by introducing a relative variance constraint on the maximum as a nonparametric complexity measure. It pioneers the application of kernel methods to this domain, constructing a linear functional optimization framework over quantile function spaces. By establishing a strong minimax duality and leveraging infinite-dimensional convex programming alongside variational analysis, the paper precisely characterizes the optimal threshold under bounded variance conditions. Key contributions include an exact performance curve under the i.i.d. setting, an asymptotically optimal threshold for finite horizons, closed-form solutions for non-i.i.d. cases, and a rigorous separation of the performance bounds between the prophet-secretary model and the i.i.d. benchmark.

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