Parallel Bayesian policies for finite-horizon multiple comparisons with a known standard

We consider the problem of multiple comparisons with a known standard, in which we wish to allocate simulation effort efficiently across a finite number of simulated systems, to determine which systems have mean performance exceeding a known threshold. We suppose that parallel computing resources are available, and that we are given a fixed simulation budget. We consider this problem in a Bayesian setting, and formulate it as a stochastic dynamic program. For simplicity, we focus on Bernoulli sampling, with a linear loss function. Using links to restless multi-armed bandits, we provide a computationally tractable upper bound on the value of the Bayes-optimal policy, and an index policy motivated by these upper bounds.