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 a well-defined 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 additional conditions on the post-change family of distributions, it is shown that the proposed algorithm is asymptotically optimal, uniformly for all possible post-change distributions.
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