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One Sample Suffices for Matroid Prophet Inequalities against an Almighty Adversary

OpenAI

OpenAI Mathopenai-math/One-Sample-Suffices-for-Matroid-Prophet-Inequalities-against-an-Almighty-AdversarySep 23, 2026cs.CCAI-generatedscore 0

We prove that one independent sample per element suffices for a constant-competitive prophet inequality on every finite matroid. The guarantee holds even when the arrival-order adversary observes all samples, all online values, and the algorithm's entire random seed. The rule needs no description of the value distributions and achieves the absolute competitive ratio $2^{-310}$.

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