  Stochastic high dimensional bandit problems with low dimensional structure
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 best regret bounds in the LASSO
bandit, better bounds in the low-rank matrix bandit and the group sparse matrix
bandit, as well as a novel bound in the multi-agent LASSO bandit.
