Asymptotic randomised control with applications to bandits
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 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.
Fields of Study & Subjects
Advanced Bandit Algorithms Research
Smart Grid Energy Management
Reinforcement Learning in Robotics
Publication details
- Journal / source
- Numerical Algebra Control and Optimization
- Publisher
- American Institute of Mathematical Sciences (AIMS)
- Volume
- 19
- Issue
- 0
- Pages
- 133–167
- Publication date
- 1 January 2026
- Language
- EN