Non-Parametric Stochastic Sequential Assignment With Random Arrival Times

TL;DR

This paper introduces NPSA, a non-parametric algorithm for sequential job acceptance with random arrivals and values, demonstrating convergence to optimal reward as data increases, validated on synthetic and real datasets.

Contribution

The paper proposes the NPSA algorithm for non-parametric sequential assignment with random arrivals, proving its convergence to optimality with increasing data.

Findings

NPSA converges in probability to optimal reward as data size grows.

Empirical validation shows NPSA performs well on synthetic and fraud detection datasets.

The approach handles unknown arrival distributions without parametric assumptions.

Abstract

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.