Many problems in operations and risk management require the familiar “estimate, then optimize” workflow involving a model estimation from data in the first step before plugging in the trained model to solve various optimization tasks. In this talk, we first give the ingredients for constructing locally robust optimization formulations in which the first step model estimation has no effect, locally, on the optimal solutions. Then delving specifically into optimization problems affected by tail-based data imbalance, we show that this local sensitivity translates to improved out-of-sample performance freed from the first-order impact of model errors caused by model selection and misspecification biases that are especially difficult to avoid when performing estimation with imbalanced data.  

The key ingredient in achieving this local robustness is a novel debiasing procedure that adds a non-parametric bias correction term to the objective. The debiased objective retains convexity, and the imputation of the correction term relies only on a non-restrictive large deviations behavior conducive for transferring knowledge from representative data-rich regions to the datascarce tail regions suffering from imbalance. The bias correction gets determined by the extent of model error in the estimation step and the specifics of the stochastic program in the optimization step, thereby serving as a scalable “smart-correction” step bridging the disparate goals in estimation and optimization. Besides showing the empirical effectiveness of the proposed formulation in real datasets, the numerical experiments bring out the utility of locally robust solutions in tackling model errors and shifts in distribution between training and deployment.