The Dao of Robustness

We present a general framework for data-driven optimization called robustness optimization that favors solutions for which a risk-aware objective function would best attain an acceptable target even when the actual probability distribution would deviate from the empirical distribution.  Unlike data-driven robust optimization approaches, the decision maker does not have to size the  ambiguity set, but specifies an acceptable target, or loss of optimality compared to the baseline optimization model, as a trade off for the model’s ability to withstand greater uncertainty.  We axiomatize the decision criterion associated with robustness optimization, termed as the  fragility measure  and present its representation theorem. We present practicable robustness optimization models including models with safegurarding constraints, adaptive and dynamic optimization models. Similar to robust optimization, we show that robustness optimization can also be done in a tractable way. We also provide numerical studies on adaptive problems and show that the solutions to the robustness optimization models are effective in alleviating the Optimizer’s Curse (Smith and Winkler 2006) and yielding superior out-of-sample performance compared the empirical optimization model and current data-driven robust optimization models. This is a joint work with Mingling Zhou and Zhuoyu Long.