Reviews: Variance-based Regularization with Convex Objectives

The article "Variance-based Regularization with Convex Objectives" considers the problem of the risk minimization in a wide class of parametric models. The authors propose the convex surrogate for variance which allows for the near-optimal and computationally efficient estimation. The idea of the paper is to substitute the variance term in the upper bound for the risk of estimation with the convex surrogate based on the certain robust penalty. The authors prove that this surrogate provides good approximation to the variance term and prove certain upper bounds on the overall performance of the method. Moreover, the particular example is provided where the proposed method beats empirical risk minimization. The experimental part of the paper considers the comparison of empirical risk minimization with proposed robust method on 2 classification problems.