  We advance the study of incentivized bandit exploration, in which arm choices
are viewed as recommendations and are required to be Bayesian incentive
compatible. Recent work has shown under certain independence assumptions that
after collecting enough initial samples, the popular Thompson sampling
algorithm becomes incentive compatible. We give an analog of this result for
linear bandits, where the independence of the prior is replaced by a natural
convexity condition. This opens up the possibility of efficient and
regret-optimal incentivized exploration in high-dimensional action spaces. In
the semibandit model, we also improve the sample complexity for the
pre-Thompson sampling phase of initial data collection.
