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Machine Learning (ML) increasingly informs the allocation of opportunities toindividuals and communities in areas such as lending, education, employment,and beyond. Such decisions often impact their subjects' future characteristicsand capabilities in an a priori unknown fashion. The decision-maker, therefore,faces exploration-exploitation dilemmas akin to those in multi-armed bandits.Following prior work, we model communities as arms. To capture the long-termeffects of ML-based allocation decisions, we study a setting in which thereward from each arm evolves every time the decision-maker pulls that arm. Wefocus on reward functions that are initially increasing in the number of pullsbut may become (and remain) decreasing after a certain point. We argue that anacceptable sequential allocation of opportunities must take an arm's potentialfor growth into account. We capture these considerations through the notion ofpolicy regret, a much stronger notion than the often-studied external regret,and present an algorithm with provably sub-linear policy regret forsufficiently long time horizons. We empirically compare our algorithm withseveral baselines and find that it consistently outperforms them, in particularfor long time horizons.

Addressing the Long-term Impact of ML Decisions via Policy Regret