Asymptotic Randomised Control with applications to bandits

• URL: http://arxiv.org/abs/2010.07252v2
• Date: Sat, 3 Sep 2022 21:54:38 GMT
• Title: Asymptotic Randomised Control with applications to bandits
• Authors: Samuel N. Cohen and Tanut Treetanthiploet
• Abstract summary: We consider a general multi-armed bandit problem with correlated elements as a relaxed control problem. By introducing an entropy regularisation, we obtain a smooth approximation to the value function. This yields a novel semi-index approximation of the optimal decision process.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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