Improving the Knowledge Gradient Algorithm

Le Yang, Siyang Gao, Chin Pang Ho

Keywords: best arm identification, knowledge gradient, asymptotic optimality, convergence rate

TL;DR: In this research, we show drawbacks of the knowledge gradient algorithm, a popular police designed for the best arm identification problem, and propose an improved version of the algorithm that can avoid those drawbacks.

Abstract: 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. In this research, we show that this policy has limitations, causing the algorithm not asymptotically optimal. We next provide a remedy for it, by following the manner of one-step look ahead of KG, but instead choosing the measurement that yields the greatest one-step improvement in the probability of selecting the best arm. The new policy is called improved knowledge gradient (iKG). iKG can be shown to be asymptotically optimal. In addition, we show that compared to KG, it is easier to extend iKG to variant problems of BAI, with the $\epsilon$-good arm identification and feasible arm identification as two examples. The superior performances of iKG on these problems are further demonstrated using numerical examples.

Submission Number: 12429