From Data to Uncertainty Sets: a Machine Learning Approach
This addresses the issue of high constraint violation probabilities in optimization models for practitioners in fields like operations research, though it is incremental as it builds on existing robust optimization methods.
The paper tackles the problem of uncertain constraints in prescriptive analytics by using robust optimization to design uncertainty sets based on a machine learning model's loss function, resulting in uncertainty sets with radii up to one order of magnitude smaller than other approaches in synthetic experiments.
Existing approaches of prescriptive analytics -- where inputs of an optimization model can be predicted by leveraging covariates in a machine learning model -- often attempt to optimize the mean value of an uncertain objective. However, when applied to uncertain constraints, these methods rarely work because satisfying a crucial constraint in expectation may result in a high probability of violation. To remedy this, we leverage robust optimization to protect a constraint against the uncertainty of a machine learning model's output. To do so, we design an uncertainty set based on the model's loss function. Intuitively, this approach attempts to minimize the uncertainty around a prediction. Extending guarantees from the robust optimization literature, we derive strong guarantees on the probability of violation. On synthetic computational experiments, our method requires uncertainty sets with radii up to one order of magnitude smaller than those of other approaches.