  Bandit learning is characterized by the tension between long-term exploration
and short-term exploitation. However, as has recently been noted, in settings
in which the choices of the learning algorithm correspond to important
decisions about individual people (such as criminal recidivism prediction,
lending, and sequential drug trials), exploration corresponds to explicitly
sacrificing the well-being of one individual for the potential future benefit
of others. This raises a fairness concern. In such settings, one might like to
run a "greedy" algorithm, which always makes the (myopically) optimal decision
for the individuals at hand - but doing this can result in a catastrophic
failure to learn. In this paper, we consider the linear contextual bandit
problem and revisit the performance of the greedy algorithm. We give a smoothed
analysis, showing that even when contexts may be chosen by an adversary, small
perturbations of the adversary's choices suffice for the algorithm to achieve
"no regret", perhaps (depending on the specifics of the setting) with a
constant amount of initial training data. This suggests that "generically"
(i.e. in slightly perturbed environments), exploration and exploitation need
not be in conflict in the linear setting.
