Data-Efficient Minimax Quickest Change Detection with Composite Post-Change Distribution

The problem of quickest change detection is studied, where there is an additional constraint on the cost of observations used before the change point and where the post-change distribution is composite. Minimax formulations are proposed for this problem. It is assumed that the post-change family of distributions has a member which is least favorable in some sense. An algorithm is proposed in which on-off observation control is employed using the least favorable distribution, and a generalized likelihood ratio based approach is used for change detection. Under the additional condition that either the post-change family of distributions is finite, or both the pre- and post-change distributions belong to a one parameter exponential family, it is shown that the proposed algorithm is asymptotically optimal, uniformly for all possible post-change distributions.