  Thompson Sampling is a well established approach to bandit and reinforcement
learning problems. However its use in continuum armed bandit problems has
received relatively little attention. We provide the first bounds on the regret
of Thompson Sampling for continuum armed bandits under weak conditions on the
function class containing the true function and sub-exponential observation
noise. Our bounds are realised by analysis of the eluder dimension, a recently
proposed measure of the complexity of a function class, which has been
demonstrated to be useful in bounding the Bayesian regret of Thompson Sampling
for simpler bandit problems under sub-Gaussian observation noise. We derive a
new bound on the eluder dimension for classes of functions with Lipschitz
derivatives, and generalise previous analyses in multiple regards.
