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Asymptotically Optimal Learning for Parametric Prophet In...
[Submitted on 25 Jun 2026] · 2026-06-26 · via stat updates on arXiv.org

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Abstract:We study learning in prophet inequalities with i.i.d. rewards drawn from an exponential-type parametric family with an unknown parameter $\theta$, a class that includes exponential, Pareto, and bounded-support power-family distributions. We first characterize the optimal full-information asymptotic competitive ratio for this family. In the unbounded-support case, the limit is $ {\left({\theta}/({\theta-c_+})\right)^{c_+/\theta}}/ {\Gamma(1-c_+/\theta)},$ while in the bounded-support case, the limit is $1$. We then propose a confidence-based dynamic-programming policy for online learning. By exploiting the explicit parametric structure, the policy achieves the same optimal asymptotic competitive ratio using only online observations, without external offline samples. We further derive distribution-specific convergence rates for canonical examples. Finally, numerical experiments on synthetic instances illustrate the performance of our algorithm.

Submission history

From: Jung-Hun Kim [view email]
[v1] Thu, 25 Jun 2026 11:26:16 UTC (93 KB)

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