Should I Stalk or Should I Go? An Auditing Exploration/Exploitation Dilemma

We consider a fraud inspection problem where service providers are central to the fraud generating process, either as the main protagonists or as colluding third parties. Because interactions are repeated between the auditor (insurer, tax collector , environmental regulation agency, etc.) and auditees (doctors, tax preparers, waste management subcontractors, etc.), auditing behaves as a learning mechanism to separate the wheat (honest agents) from the chaff (defrauders). We analyze a Bayesian inspector's dynamic auditing problem in the face of fraud, and characterize its optimal strategy as a strategic exploration/one-armed bandit one. The insurer faces the well-known reinforcement learning exploration/exploitation trade-off between gathering information for higher future profits (exploration) and prioritizing immediate profits (exploitation). We then derive optimal auditing strategies with multiple auditees and capacity constraints as the solution to a k-armed bandit problem. We finally investigate the extents to which learning occurs under optimality in terms of how much information is obtained and how quickly it is obtained.