A Simple Unified Framework for High Dimensional Bandit Problems

TL;DR

This paper introduces a simple, unified algorithm for high-dimensional bandit problems that leverages low-dimensional structures to achieve competitive regret bounds across various problem settings.

Contribution

It presents a general analysis framework and a versatile algorithm applicable to multiple high-dimensional bandit scenarios, including new problem types.

Findings

Achieves regret bounds comparable to existing methods in LASSO bandits.

Provides novel regret bounds for low-rank and group sparse matrix bandits.

Introduces a multi-agent LASSO bandit problem with effective solutions.

Abstract

Stochastic high dimensional bandit problems with low dimensional structures are useful in different applications such as online advertising and drug discovery. In this work, we propose a simple unified algorithm for such problems and present a general analysis framework for the regret upper bound of our algorithm. We show that under some mild unified assumptions, our algorithm can be applied to different high dimensional bandit problems. Our framework utilizes the low dimensional structure to guide the parameter estimation in the problem, therefore our algorithm achieves the comparable regret bounds in the LASSO bandit, as well as novel bounds in the low-rank matrix bandit, the group sparse matrix bandit, and in a new problem: the multi-agent LASSO bandit.