Consistency of Sequential Bayesian Sampling Policies

Consistency of Sequential Bayesian Sampling Policies

We consider Bayesian information collection, in which a measurement policy collects information to support a future decision. This framework includes ranking and selection, continuous global optimization, and many other problems in sequential experimental design. We give a sufficient condition under which measurement policies sample each measurement type infinitely often, ensuring consistency, ...

Asymptotic Optimality of Sequential Sampling Policies for Bayesian Information Collection

We consider adaptive sequential sampling policies in a Bayesian framework. Under the assumptions that the sampling distribution is from an exponential family and that the number of distinct measurement types is finite, we give sufficient conditions for an adaptive sampling policy to achieve asymptotic optimality. Here, asymptotic optimality is understood to mean that the limit of the expected l...

Convergence to Global Optimality with Sequential Bayesian Sampling Policies

We consider Bayesian information collection, in which a measurement policy collects information to support a future decision. This framework includes problems in ranking and selection, reinforcement learning, and continuous global optimization. We give sufficient conditions under which measurement policies achieve asymptotically minimal expected loss. Achieving asymptotically minimal expected l...

Optimality of index policies for a sequential sampling problem

Consider the following sequential sampling problem: at each time, a choice must be made between obtaining an independent sample from one of a set of random reward variables or stopping the sampling. Sampling a random variable incurs a random cost at each time. The objective of the problem is to maximize the expected net difference between the largest sample reward obtained before stopping and t...

On Bayesian index policies for sequential resource allocation