Expected lossIt is the predictive ability of all samples and is a global concept. Empirical risk is a local concept and only represents the predictive ability of the decision function for samples in the training data set.

Empirical risk and expected risk

The empirical risk is local. Based on minimizing the loss function of all sample points in the training set, the empirical risk is locally optimal and can be realistically obtained.

The expected risk is global. Based on minimizing the loss function of all sample points, the expected risk is globally optimal and idealization cannot be achieved.

References

【1】Machine Learning Optimization Problems - Empirical Risk, Expected Risk, Structural Risk