Using Cache or Credit for Parallel Ranking and Selection

In this paper, we focus on ranking and selection procedures that sequentially allocate replications to systems by applying some acquisition function. We propose an acquisition function, called gCEI, which exploits the gradient of the complete expected improvement with respect to the number of replications. We prove that the gCEI procedure, which adopts gCEI as the acquisition function in a serial computing environment, achieves the asymptotically optimal static replication allocation of Glynn and Juneja in the limit under a normality assumption. We also propose two procedures, called caching and credit, that extend any acquisition-function-based procedure in a serial environment into both synchronous and asynchronous parallel environments. While allocating replications to systems, both procedures use persistence forecasts for the unavailable outputs of the currently running replications, but differ in usage of the available outputs. We prove that under certain assumptions, the caching procedure achieves the same asymptotic allocation as in the serial environment. A similar result holds for the credit procedure using gCEI as the acquisition function. In terms of efficiency and effectiveness, the credit procedure empirically performs as well as the caching procedure despite not carefully controlling the output history as the caching procedure does, and is faster than the serial version without any number-of-replications penalty due to using persistence forecasts. Both procedures are designed to solve small-to-medium-sized problems on computers with a modest number of processors, such as laptops and desktops as opposed to high-performance clusters, and are superior to state-of-the-art parallel procedures in this setting.