  The Asymptotic Randomised Control (ARC) algorithm provides a rigorous
approximation to the optimal strategy for a wide class of Bayesian bandits,
while retaining reasonable computational complexity. In particular, it allows a
decision maker to observe signals in addition to their rewards, to incorporate
correlations between the outcomes of different choices, and to have nontrivial
dynamics for their estimates. The algorithm is guaranteed to asymptotically
optimise the expected discounted payoff, with error depending on the initial
uncertainty of the bandit. In this paper, we consider a batched bandit problem
where observations arrive from a generalised linear model; we extend the ARC
algorithm to this setting. We apply this to a classic dynamic pricing problem
based on a Bayesian hierarchical model and demonstrate that the ARC algorithm
outperforms alternative approaches.
