{"abstract":"Many real-world analytics problems involve two significant challenges:\nprediction and optimization. Due to the typically complex nature of each\nchallenge, the standard paradigm is predict-then-optimize. By and large,\nmachine learning tools are intended to minimize prediction error and do not\naccount for how the predictions will be used in the downstream optimization\nproblem. In contrast, we propose a new and very general framework, called Smart\n\"Predict, then Optimize\" (SPO), which directly leverages the optimization\nproblem structure, i.e., its objective and constraints, for designing better\nprediction models. A key component of our framework is the SPO loss function\nwhich measures the decision error induced by a prediction.\n Training a prediction model with respect to the SPO loss is computationally\nchallenging, and thus we derive, using duality theory, a convex surrogate loss\nfunction which we call the SPO+ loss. Most importantly, we prove that the SPO+\nloss is statistically consistent with respect to the SPO loss under mild\nconditions. Our SPO+ loss function can tractably handle any polyhedral, convex,\nor even mixed-integer optimization problem with a linear objective. Numerical\nexperiments on shortest path and portfolio optimization problems show that the\nSPO framework can lead to significant improvement under the\npredict-then-optimize paradigm, in particular when the prediction model being\ntrained is misspecified. We find that linear models trained using SPO+ loss\ntend to dominate random forest algorithms, even when the ground truth is highly\nnonlinear.","author":[{"family":"Elmachtoub"},{"family":"Grigas"}],"id":"unknown","issued":{"date-parts":[[2020,11,19]]},"language":"en","title":"Smart \"Predict, then Optimize\"","type":"article"}