Envious Explore and Exploit

Explore-and-exploit tradeoffs play a key role in recommendation systems (RSs), aiming at serving users better by learning from previous interactions. Despite their commercial success, the societal effects of explore-and-exploit mechanisms are not well understood, especially regarding the utility discrepancy they generate between different users. In this work, we measure such discrepancy using the economic notion of envy. We present a multi-armed bandit-like model in which every round consists of several sessions, and rewards are realized once per round. We call the latter property reward consistency, and show that the RS can leverage this property for better societal outcomes. On the downside, doing so also generates envy, as late-to-arrive users enjoy the information gathered by early-to-arrive users. We examine the generated envy under several arrival order mechanisms and virtually any anonymous algorithm, i.e., any algorithm that treats all similar users similarly without leveraging their identities. We provide tight envy bounds on uniform arrival and upper bound the envy for nudged arrival, in which the RS can affect the order of arrival by nudging its users. Furthermore, we study the efficiency-fairness trade-off by devising an algorithm that allows constant envy and approximates the optimal welfare in restricted settings. Finally, we validate our theoretical results empirically using simulations.