On regularization schemes for data-driven optimization based on Cressie-Read divergence and CVaR

This paper presents several regularization schemes for data-driven optimization problems. Data-driven optimization is a challenging task because the model or the distribution describing the inherent stochastic disturbance is unknown but instead only a set of data sampled from it can be available. How to explore these data rather than the exact model of the optimization function to aid the optimization analysis becomes increasingly important in the modern big-data era. Empirical risk minimization is usually not satisfactory due to its over-fitting side effect. Regularization is a good option to combat over-fitting. By constructing Cressie-Read divergence-based ambiguity set as well as ratio-deviation based ambiguity set and by employing the distributionally robust optimization approach, a couple of regularization schemes for data-driven problems are proposed. These regularization schemes improve the popular mean-variance regularization which unfortunately leads to non-convex optimization. A linkage is also explored between the proposed regularization schemes and the classical conditional-value-at-risk problem.