  We investigate properties of Thompson Sampling in the stochastic multi-armed
bandit problem with delayed feedback. In a setting with i.i.d delays, we
establish to our knowledge the first regret bounds for Thompson Sampling with
arbitrary delay distributions, including ones with unbounded expectation. Our
bounds are qualitatively comparable to the best available bounds derived via
ad-hoc algorithms, and only depend on delays via selected quantiles of the
delay distributions. Furthermore, in extensive simulation experiments, we find
that Thompson Sampling outperforms a number of alternative proposals, including
methods specifically designed for settings with delayed feedback.
