A predictive look at Bayesian Bandits

A multi-armed bandit problem models an agent that simultaneously attempts to acquire new information (exploration) and optimizes the decisions based on existing knowledge (exploitation). In clinical trials, this framework applies to Bayesian multi-armed randomized adaptive designs. The allocation rule of experimental units involves the posterior probability of each treatment being the best. The trade-off between gain in information and selection of the most promising treatment is modulated by a quantity γ, typically prefixed or linearly increasing with accumulating sample size. We propose a predictive criterion for selecting γ that also allows its progressive reassessment based on interim analyses data.