To obtain the upper bound of Equation (10), we consider the second-order taylor expansion for L(c(z1),(p1+p2)/2)andL(c(z2),(p1+p2)/2)givenby L c(z1), p1+p2 2 L

Medical Expenditure Dataset (MEPS4): This is used to predict whether a person has high utilizationornot. Fortabular datasets, weuse the batch size of 64, and train the model for a maximum of 20 epochs. Adversarial Training (Adversarial): Consider that the classification model isf(x) = c(g(x)) where g(x) is the encoder andc() is the classification head. For adversarial training, another adversarial classifiercadv()is also constructed. The classification headc()and the adversarial classifier cadv() are trained simultaneously.