Optimal Measurement Sequencing in M-Ary Hypothesis Testing Problems

In this paper, we formulate and solve a sequential decision problem of a special type arising in M-ary hypothesis testing. In this problem, a team, comprised of a primary decisionmaker (DM) and N geographically separated subordinate DMs, is faced with the task of deciding which one of the M prespecified hypotheses is true, subject to the constraint that the team is allowed to make at most K measurement. The subordinate DMs serve as information sources for the primary DM. At each stage k, k = 1,2,.., K of the decision process, the primary DM decides which subordinate DM should observe and send the measurement. When the information seeking process terminates, the primary DM makes a decision for the team as to which hypothesis is true. The objective of the team is to maximize the probability of correct decision after K measurements. In this paper, we develop measurement sequencing strategies based on dynamic programming (DP), and a computationally efficient greedy algorithm for this problem. Numerical results show that the performance of greedy measurement sequencing strategy is within 1% of the optimal DP strategy.