On parallel policies for ranking and selection problems

In this paper we develop and test experimental methodologies for selection of the best alternative among a discrete number of available treatments. We consider a scenario where a researcher sequentially decides which treatments are assigned to experimental units. This problem is particularly challenging if a single measurement of the response to a treatment is time-consuming and there is a limited time for experimentation. This time can be decreased if it is possible to perform measurements in parallel. In this work we propose and discuss asynchronous extensions of two well-known Ranking & Selection policies, namely, Optimal Computing Budget Allocation (OCBA) and Knowledge Gradient (KG) policy. Our extensions (Asynchronous Optimal Computing Budget Allocation (AOCBA) and Asynchronous Knowledge Gradient (AKG), respectively) allow for parallel asynchronous allocation of measurements. Additionally, since the standard KG method is sequential (it can only allocate one experiment at a time) we propose a parallel synchronous extension of KG policy – Synchronous Knowledge Gradient (SKG). Computer simulations of our algorithms indicate that our parallel KG-based policies (AKG, SKG) outperform the standard OCBA method as well as AOCBA, if the number of evaluated alternatives is small or the computing/experimental budget is limited. For experimentations with large budgets and big sets of alternatives, both the OCBA and AOCBA policies are more efficient.