Asymptotic Randomised Control with applications to bandits

TL;DR

This paper introduces Asymptotic Randomised Control (ARC), a novel approach for correlated multi-armed bandit problems that uses entropy regularisation to approximate the optimal policy and balance exploration and exploitation effectively.

Contribution

It proposes a semi-index approximation method for the control problem, providing a new way to handle correlation and non-linearity in bandit environments.

Findings

ARC algorithm performs well compared to existing methods

The semi-index balances exploration and exploitation explicitly

Entropy regularisation leads to smooth value function approximation

Abstract

We consider a general multi-armed bandit problem with correlated (and simple contextual and restless) elements, as a relaxed control problem. By introducing an entropy regularisation, we obtain a smooth asymptotic approximation to the value function. This yields a novel semi-index approximation of the optimal decision process. This semi-index can be interpreted as explicitly balancing an exploration-exploitation trade-off as in the optimistic (UCB) principle where the learning premium explicitly describes asymmetry of information available in the environment and non-linearity in the reward function. Performance of the resulting Asymptotic Randomised Control (ARC) algorithm compares favourably well with other approaches to correlated multi-armed bandits.