  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.
