Abstract

The problem of multihypothesis 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 reduce the delay by intelligently choosing the control for observation collection in each time slot. A policy for this problem is derived that satisfies given constraints on the error probability, and it is shown that this policy is asymptotically optimal in the sense that it asymptotically achieves an information-theoretic lower bound on the expected delay. Numerical results are provided that illustrate an application of the policy to medical diagnostic inference.

摘要

考虑了对观察的受控感知进行多假设检验的问题。假设在每个控制下收集的观测值分布遵循单参数指数族分布。目标是设计一种策略，以最小预期延迟找到真实假设，同时确保错误概率低于给定约束。决策者可以通过智能选择每个时隙的观测采集控制来减少延迟。推导出此问题的策略，该策略满足错误概率的给定约束，并且表明该策略是渐近最优的，因为它渐近实现了预期延迟的信息理论下界。