Greedy Algorithm Almost Dominates in Smoothed Contextual Bandits

Abstract

Online learning algorithms, widely used to power search and content optimization onthe web, must balance exploration and exploitation, potentially sacrificing the experience of currentusers in order to gain information that will lead to better decisions in the future. While necessary inthe worst case, explicit exploration has a number of disadvantages compared to the greedy algorithmthat always ``exploits"" by choosing an action that currently looks optimal. We determine under whatconditions inherent diversity in the data makes explicit exploration unnecessary. We build on a recentline of work on the smoothed analysis of the greedy algorithm in the linear contextual bandits model.We improve on prior results to show that the greedy algorithm almost matches the best possibleBayesian regret rate of any other algorithm on the same problem instance whenever the diversityconditions hold. The key technical finding is that data collected by the greedy algorithm sufficesto simulate a run of any other algorithm. Further, we prove that under a particular smoothnessassumption, the Bayesian regret of the greedy algorithm is at most \~O(T 1/3) in the worst case, whereT is the time horizon.