Asymptotic randomised control with applications to bandits

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 premium, 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 UCB (Upper Confidence Bound) 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.