In a multi-armed bandit (MAB) problem, an online algorithm makes a sequence of choices. In each round it chooses from a time-invariant set of alternatives and receives the payoff associated with this alternative. While the case of small strategy sets is by now well-understood, a lot of recent work has focused on MAB problems with exponentially or infinitely large strategy sets, where one needs to assume extra structure in order to make the problem tractable. In particular, recent literature considered information on similarity between arms. We consider similarity information in the setting of contextual bandits, a natural extension of the basic MAB problem where before each round an algorithm is given the context -a hint about the payoffs in this round. Contextual bandits are directly motivated by placing advertisements on webpages, one of the crucial problems in sponsored search. A particularly simple way to represent similarity information in the contextual bandit setting is via a similarity distance between the context-arm pairs which gives an upper bound on the difference between the respective expected payoffs. Prior work on contextual bandits with similarity uses "uniform" partitions of the similarity space, so that, essentially, each context-arm pair is approximated by the closest pair in the partition. Algorithms based on "uniform" partitions disregard the structure of the payoffs and the context arrivals. This is potentially wasteful, as it may be advantageous to maintain a finer partition in high-payoff regions of the similarity space and popular regions of the context space. In this paper, we design algorithms that are based on adaptive partitions which are adjusted to the popular and high-payoff regions, and thus can take advantage of the problem instances with "benign" payoffs or context arrivals.
Also related are results on contextual bandits with similarity information on the contexts, which automatically encodes a potentially easier learning problem REF .
Contextual Bandits with Similarity Information
ArXiv
ArXiv
Mathematics Computer Science