A quickest change detection problem is studied where the decision-maker has access to multiple experiments, but can choose only one experiment at a time to detect the change. The true post-change distribution under each experiment is unknown, but known to belong to a family of distributions. It is assumed that each of these families of distributions has an element that is least favorable in a well-defined sense. An algorithm is proposed that is designed using the least favorable distributions. It is shown that the algorithm is first-order asymptotically optimal, as the rate of false alarms goes to zero. This algorithm minimizes the worst-case average detection delay over all post-change distributions within the assumed families, subject to a constraint on the average run length to false alarm and constraints on the average fraction of time each experiment is performed before change.

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