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

TL;DR

This paper extends the ARC algorithm to handle correlated, batched, and generalized linear model observations in Bayesian bandits, demonstrating improved performance in dynamic pricing applications.

Contribution

It introduces a large sample approximation for correlated, batched observations within the ARC framework, applied to dynamic pricing with superior results.

Findings

ARC outperforms alternative methods in dynamic pricing.

The extended ARC handles correlated and batched observations effectively.

The approach guarantees asymptotic optimality with manageable error.

Abstract

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.