  The Asymptotic Randomised Control (ARC) algorithm provides a rigorous
approximation to the optimal strategy for a wide class of Bayesian bandits,
while retaining low computational complexity. In particular, the ARC approach
provides nearly optimal choices even when the payoffs are correlated or more
than the reward is observed. 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 extend the ARC framework to
consider a batched bandit problem where observations arrive from a generalised
linear model. In particular, we develop a large sample approximation to allow
correlated and generally distributed observation. We apply this to a classic
dynamic pricing problem based on a Bayesian hierarchical model and demonstrate
that the ARC algorithm outperforms alternative approaches.
