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We consider a problem wherein jobs arrive at random times and assume randomvalues. Upon each job arrival, the decision-maker must decide immediatelywhether or not to accept the job and gain the value on offer as a reward, withthe constraint that they may only accept at most $n$ jobs over some referencetime period. The decision-maker only has access to $M$ independent realisationsof the job arrival process. We propose an algorithm, Non-Parametric SequentialAllocation (NPSA), for solving this problem. Moreover, we prove that theexpected reward returned by the NPSA algorithm converges in probability tooptimality as $M$ grows large. We demonstrate the effectiveness of thealgorithm empirically on synthetic data and on public fraud-detection datasets,from where the motivation for this work is derived.

Non-Parametric Stochastic Sequential Assignment With Random Arrival Times