Nonlinear Distributionally Robust Optimization

Understand

This article focuses on a class of distributionally robust optimization (DRO) problems where, unlike the growing body of the literature, the objective function is potentially nonlinear in the distribution.

• Existing methods to optimize nonlinear functions in probability space use the Frechet derivatives, which present theoretical and computational challenges.
• Motivated by this, we propose an alternative notion for the derivative and corresponding smoothness based on Gateaux (G)-derivative for generic risk measures.
• These concepts are explained via three running risk measure examples of variance, entropic risk, and risk on finite support sets.