POMDP-Based Ranking and Selection

In this paper, we formulate the ranking and selection (R&S) problem as a stochastic control problem under the Bayesian framework. We propose to use particle filter to approximate the posterior distribution of states under the general Bayesian framework. The learning and decision are treated under the umbrella of a partially observable Markov decision process and a rollout policy based on Monte Carlo simulation is proposed. This policy can use one or more classic R&S approaches as base policies to efficiently learn the value function by rolling out simulation trajectories. We present numerical examples to demonstrate the effectiveness of the rollout policy and the performance of our policy is significantly improved relatively to the base policies.