We consider a standard Bayes decision situation except that with small probability the data may be irrelevant to the parameter of interest (i.e. the experiment is "biased"). The minimax solution under quite general assumptions is described and discussed.
Ya'acov Ritov. "Robust Bayes Decision Procedures: Gross Error in the Data Distribution." Ann. Statist. 13 (2) 626 - 637, June, 1985. https://doi.org/10.1214/aos/1176349543