Instead of minimizing the maximum risk it is proposed to restrict attention to decision procedures whose maximum risk does not exceed the minimax risk by more than a given amount. Subject to this restriction one may wish to minimize the average risk with respect to some guessed a priori distribution suggested by previous experience. It is shown how Wald's minimax theory can be modified to yield analogous results concerning such restricted Bayes solutions. A number of examples are discussed, and some extensions of the above criterion are briefly considered.
"The use of Previous Experience in Reaching Statistical Decisions." Ann. Math. Statist. 23 (3) 396 - 407, September, 1952. https://doi.org/10.1214/aoms/1177729384