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Equivalence of the Empirical Risk Minimization to Regularization on the Family of f-Divergences
The solution to empirical risk minimization with $f$-divergence regularization (ERM-$f$DR) is presented under mild conditions on $f$.
Analysis of the Relative Entropy Asymmetry in the Regularization of Empirical Risk Minimization
The analysis of the solution unveils the following properties of relative entropy when it acts as a regularizer in the ERM-RER problem: i) relative entropy forces the support of the Type-II solution to collapse into the support of the reference measure, which introduces a strong inductive bias that dominates the evidence provided by the training data; ii) Type-II regularization is equivalent to classical relative entropy regularization with an appropriate transformation of the empirical risk function.
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