Data-efficient quickest change detection with unknown 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 unknown. An algorithm is proposed for the case where there are finite number of possibilities for the unknown post-change distribution. It is shown that if the post-change family of distributions satisfies some additional conditions, then the proposed algorithm is asymptotically optimal uniformly for all possible post-change distributions.