The theoretical and empirical performance of Empirical Risk Minimization (ERM) often suffers when loss functions are poorly behaved with large Lipschitz moduli spurious sharp minimizers. We propose analyze a counterpart to ERM called Diametrical (DRM), which accounts for worst-case risks within neighborhoods in parameter space. DRM has generalization bounds that independent convex as well nonco...

The Vicinal Risk Minimization principle establishes a bridge between generative models and methods derived from the Structural Risk Minimization Principle such as Support Vector Machines or Statistical Regularization. We explain how VRM provides a framework which integrates a number of existing algorithms, such as Parzen windows, Support Vector Machines, Ridge Regression, Constrained Logistic C...

We develop a learning principle and an efficient algorithm for batch learning from logged bandit feedback. Unlike in supervised learning, where the algorithm receives training examples (xi, y ∗ i ) with annotated correct labels y ∗ i , bandit feedback merely provides a cardinal reward δi ∈ R for the prediction yi that the logging system made for context xi. Such bandit feedback is ubiquitous in...

The problem of ranking (rank regression) has become popular in the machine learning community. This theory relates to problems, in which one has to predict (guess) the order between objects on the basis of vectors describing their observed features. In many ranking algorithms a convex loss function is used instead of the 0−1 loss. It makes these procedures computationally efficient. Hence, conv...

In this paper we study the differentially private Empirical Risk Minimization (ERM) problem in different settings. For smooth (strongly) convex loss function with or without (non)-smooth regularization, we give algorithms that achieve either optimal or near optimal utility bounds with less gradient complexity compared with previous work. For ERM with smooth convex loss function in high-dimensio...