Asymptotic Randomised Control with applications to bandits
This work addresses the challenge of correlated bandits for researchers and practitioners in reinforcement learning, offering a novel method that is incremental in building on existing control and UCB principles.
The paper tackles the multi-armed bandit problem with correlated elements by formulating it as a relaxed control problem with entropy regularization, resulting in a semi-index approximation that balances exploration and exploitation. The proposed Asymptotic Randomised Control (ARC) algorithm shows favorable performance compared to other approaches.
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.