Distributionally Robust Optimization: A review on theory and applications

<p style='text-indent:20px;'>In this paper, we survey the primary research on theory and applications of distributionally robust optimization (DRO). We start with reviewing modeling power computational attractiveness DRO approaches, induced by ambiguity sets structure tractable counterpart reformulations. Next, summarize efficient solution methods, out-of-sample performance guarantee, convergence analysis. Then, illustrate some in machine learning operations research, finally, discuss future directions.</p>