Nearest Neighbour with Bandit Feedback
This work provides an efficient algorithm for contextual bandits, applicable to online classification, but it appears incremental as it builds on existing nearest neighbor methods.
The authors adapted the nearest neighbor rule to the contextual bandit problem, handling fully adversarial data with no assumptions, achieving per-trial running time polylogarithmic in trials and actions and quasi-linear space.
In this paper we adapt the nearest neighbour rule to the contextual bandit problem. Our algorithm handles the fully adversarial setting in which no assumptions at all are made about the data-generation process. When combined with a sufficiently fast data-structure for (perhaps approximate) adaptive nearest neighbour search, such as a navigating net, our algorithm is extremely efficient - having a per trial running time polylogarithmic in both the number of trials and actions, and taking only quasi-linear space. We give generic regret bounds for our algorithm and further analyse them when applied to the stochastic bandit problem in euclidean space. We note that our algorithm can also be applied to the online classification problem.