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We introduce a new setting, optimize-and-estimate structured bandits. Here, apolicy must select a batch of arms, each characterized by its own context, thatwould allow it to both maximize reward and maintain an accurate (ideallyunbiased) population estimate of the reward. This setting is inherent to manypublic and private sector applications and often requires handling delayedfeedback, small data, and distribution shifts. We demonstrate its importance onreal data from the United States Internal Revenue Service (IRS). The IRSperforms yearly audits of the tax base. Two of its most important objectivesare to identify suspected misreporting and to estimate the "tax gap" -- theglobal difference between the amount paid and true amount owed. Based on aunique collaboration with the IRS, we cast these two processes as a unifiedoptimize-and-estimate structured bandit. We analyze optimize-and-estimateapproaches to the IRS problem and propose a novel mechanism for unbiasedpopulation estimation that achieves rewards comparable to baseline approaches.This approach has the potential to improve audit efficacy, while maintainingpolicy-relevant estimates of the tax gap. This has important socialconsequences given that the current tax gap is estimated at nearly half atrillion dollars. We suggest that this problem setting is fertile ground forfurther research and we highlight its interesting challenges. The results ofthis and related research are currently being incorporated into the continualimprovement of the IRS audit selection methods.

Integrating Reward Maximization and Population Estimation: Sequential Decision-Making for Internal Revenue Service Audit Selection