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Bandit learning is characterized by the tension between long-term explorationand short-term exploitation. However, as has recently been noted, in settingsin which the choices of the learning algorithm correspond to importantdecisions about individual people (such as criminal recidivism prediction,lending, and sequential drug trials), exploration corresponds to explicitlysacrificing the well-being of one individual for the potential future benefitof others. This raises a fairness concern. In such settings, one might like torun a "greedy" algorithm, which always makes the (myopically) optimal decisionfor the individuals at hand - but doing this can result in a catastrophicfailure to learn. In this paper, we consider the linear contextual banditproblem and revisit the performance of the greedy algorithm. We give a smoothedanalysis, showing that even when contexts may be chosen by an adversary, smallperturbations of the adversary's choices suffice for the algorithm to achieve"no regret", perhaps (depending on the specifics of the setting) with aconstant amount of initial training data. This suggests that "generically"(i.e. in slightly perturbed environments), exploration and exploitation neednot be in conflict in the linear setting.

A Smoothed Analysis of the Greedy Algorithm for the Linear Contextual Bandit Problem