Contextual Bandits with Similarity Information

TL;DR

This paper introduces adaptive algorithms for contextual bandits that leverage similarity information to improve decision-making efficiency, especially in large or infinite strategy spaces, by focusing on relevant contexts and high-payoff arms.

Contribution

It proposes novel adaptive partitioning algorithms that utilize similarity information more efficiently than uniform partitioning in contextual bandit problems.

Findings

Algorithms outperform uniform partitioning methods.

Adaptive partitions focus on popular contexts and high-payoff arms.

Improved efficiency in large or infinite strategy spaces.

Abstract

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, which is potentially wasteful. We design more efficient algorithms that are based on adaptive partitions adjusted to "popular" context and "high-payoff" arms.