Sequential Controlled Sensing for Composite Multihypothesis Testing

TL;DR

This paper develops an optimal control policy for multi-hypothesis testing with controlled sensing, minimizing delay while maintaining error probability constraints, and proves its asymptotic optimality.

Contribution

It introduces a new policy for composite multihypothesis testing with controlled sensing that is asymptotically optimal in minimizing expected delay.

Findings

Policy satisfies error probability constraints.

Policy asymptotically achieves the information-theoretic lower bound.

Effective for single-parameter exponential family distributions.

Abstract

The problem of multi-hypothesis testing with controlled sensing of observations is considered. The distribution of observations collected under each control is assumed to follow a single-parameter exponential family distribution. The goal is to design a policy to find the true hypothesis with minimum expected delay while ensuring that the probability of error is below a given constraint. The decision-maker can control the delay by intelligently choosing the control for observation collection in each time slot. We derive a policy that satisfies the given constraint on the error probability. We also show that the policy is asymptotically optimal in the sense that it asymptotically achieves an information-theoretic lower bound on the expected delay.