The knowledge gradient (KG) algorithm is a popular policy for the best arm identification (BAI) problem. It is built on the simple idea of always choosing the measurement that yields the greatest expected one-step improvement in the estimate of the best mean of the arms.

We propose a novel algorithmic framework that is tractable, asymptotically consistent,andsuperiortocomparable methodsonexampleproblems.

Forouranalysis wedevise several concentration results forMarkovchains, including amaximal inequality for Markov chains, that may be of interest in their own right. As a byproduct of our analysis we also establish asymptotically optimal, finite-time guarantees for the case of multiple plays, and i.i.d.

In this paper, we propose the first re-sampling based algorithm that is asymptotically optimal for several classes of possibly un-bounded parametric distributions.