We introduce a new setting, optimize-and-estimate structured bandits. Here, a policy must select a batch of arms, each characterized by its own context, that would allow it to both maximize reward and maintain an accurate (ideally unbiased) population estimate of the reward. This setting is inherent to many public and private sector applications and often requires handling delayed feedback, small data, and distribution shifts. We demonstrate its importance on real data from the United States Internal Revenue Service (IRS). The IRS performs yearly audits of the tax base. Two of its most important objectives are to identify suspected misreporting and to estimate the "tax gap" - the global difference between the amount paid and true amount owed. We cast these two processes as a unified optimize-and-estimate structured bandit. We provide a novel mechanism for unbiased population estimation that achieves rewards comparable to baseline approaches. This approach has the potential to improve audit efficacy, while maintaining policy-relevant estimates of the tax gap. This has important social consequences given that the current tax gap is estimated at nearly half a trillion dollars. We suggest that this problem setting is fertile ground for further research and we highlight its interesting challenges.

本研究提出了一种新的优化与估计结构化赌博问题（optimize-and-estimate structured bandits）的设定，应用于美国国税局的税款欠缴率估计。研究表明，本研究的方法可以有效提高审计效率和准确性，并有效评估纳税缺口，为未来有关方案和措施提供重要参考。

集成奖励最大化和人口估计：针对国内税务局审计选择的顺序决策