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

Abstract

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. In such settings, one might like to run a ``greedy'' algorithm, which always makes the 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.