Greedy Algorithm almost Dominates in Smoothed Contextual Bandits
This work addresses the trade-off between exploration and exploitation in web-based applications like search optimization, but it is incremental as it builds on prior smoothed analysis results.
The paper tackles the problem of whether explicit exploration is necessary in online learning by analyzing the greedy algorithm in smoothed contextual bandits, showing that it nearly matches the optimal Bayesian regret rate of O(T^{1/3}) under data diversity conditions.
Online learning algorithms, widely used to power search and content optimization on the web, must balance exploration and exploitation, potentially sacrificing the experience of current users in order to gain information that will lead to better decisions in the future. While necessary in the worst case, explicit exploration has a number of disadvantages compared to the greedy algorithm that always "exploits" by choosing an action that currently looks optimal. We ask under what conditions inherent diversity in the data makes explicit exploration unnecessary. We build on a recent line of work on the smoothed analysis of the greedy algorithm in the linear contextual bandits model. We improve on prior results to show that a greedy approach almost matches the best possible Bayesian regret rate of any other algorithm on the same problem instance whenever the diversity conditions hold, and that this regret is at most $\tilde O(T^{1/3})$.