The secretary problem with backward solicitation has been studied by Yang,Joseph,Petrocceoi,Choe and Bal. The problem is put into snell frame,the relative rank yk is replaced by the relatively best position function. Optimal stopping rules are obtained with differential probability of backward solicitation.
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Jin Zhiming, Li Xiaojie. A Secretary Problem with Backward Solicitation[J]. Journal of National University of Defense Technology,1992,14(1):76-85.