At first, this may appear rather different from the Bayes rule approach of the previous section, not a generalization. However, notice that the Bayes risk already averages over formula_31 in Bayesian fashion, and the Bayes risk may be recovered as the expectation over formula_2 of the expected loss (where formula_57 and formula_58). Roughly speaking, formula_19 minimizes this expectation of expected loss (i.e., is a Bayes rule) if and only if it minimizes the expected loss for each formula_16 separately (i.e., is a generalized Bayes rule).