Paper:
Variance-based Regularization with Convex Objectives
We develop an approach to risk minimization and stochastic optimization that provides a convex surrogate for variance, allowing near-optimal and computationally efficient trading between approximation and estimation error. Our approach builds off of techniques for distributionally robust optimization and Owen's empirical likelihood, and we provide a number of finite-sample and asymptotic results characterizing the theoretical performance of the estimator. In particular, we show that our procedure comes with certificates of optimality, achieving (in some scenarios) faster rates of convergence than empirical risk minimization by virtue of automatically balancing bias and variance. We give corroborating empirical evidence showing that in practice, the estimator indeed trades between variance and absolute performance on a training sample, improving out-of-sample (test) performance over standard empirical risk minimization for a number of classification problems.

Review:
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. The results show the expected bahaviour, i.e. the proposed method is better than ERM on rare classes with not significant loss on more common classes.
To sum up, I think that this is very strong work on the edge between the theoretical and practical machine learning. My only concern is that the paper includes involved theoretical analysis and is much more suitable for full journal publication than for short conference paper (the Arxiv paper is 47 pages long!!!).