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