  In this paper, we investigate the impact of context diversity on stochastic
linear contextual bandits. As opposed to the previous view that contexts lead
to more difficult bandit learning, we show that when the contexts are
sufficiently diverse, the learner is able to utilize the information obtained
during exploitation to shorten the exploration process, thus achieving reduced
regret. We design the LinUCB-d algorithm, and propose a novel approach to
analyze its regret performance. The main theoretical result is that under the
diverse context assumption, the cumulative expected regret of LinUCB-d is
bounded by a constant. As a by-product, our results improve the previous
understanding of LinUCB and strengthen its performance guarantee.
