Multi-Armed Bandit (UCB, Thompson Sampling)

The multi-armed bandit (MAB) is an adaptive experimental framework that allocates trials sequentially across competing arms to minimise cumulative regret while simultaneously learning which arm performs best. Formalised by Robbins in 1952 and given finite-time guarantees by Auer et al. (2002), it balances exploration of uncertain options against exploitation of currently known best options — outperforming classical A/B testing whenever early stopping or cost-sensitive allocation matters.