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The Asymptotic Randomised Control (ARC) algorithm provides a rigorousapproximation to the optimal strategy for a wide class of Bayesian bandits,while retaining low computational complexity. In particular, the ARC approachprovides nearly optimal choices even when the payoffs are correlated or morethan the reward is observed. The algorithm is guaranteed to asymptoticallyoptimise the expected discounted payoff, with error depending on the initialuncertainty of the bandit. In this paper, we extend the ARC framework toconsider a batched bandit problem where observations arrive from a generalisedlinear model. In particular, we develop a large sample approximation to allowcorrelated and generally distributed observation. We apply this to a classicdynamic pricing problem based on a Bayesian hierarchical model and demonstratethat the ARC algorithm outperforms alternative approaches.

Generalised correlated batched bandits via the ARC algorithm with application to dynamic pricing