9 Regularization via Smart Predict-then-Optimize
- The Smart Predict-then-Optimize (SPO) framework
- The SPO loss function, its unambiguous variation, and the SPO+ loss function as a convex approximation
- The end-to-end predict-then-optimize training framework that embeds an optimization block in a neural network to direct param eter updates toward a lower decision error instead of (merely) a lower prediction error
9.1 Introducing Smart Predict-then-Optimize
9.1.1 Contextual optimization
9.1.2 The shortest path problem
9.1.3 Solving the shortest path problem
9.1.4 Predict-then-optimize with unknown linear objectives
9.1.5 The SPO loss function
9.1.6 The unambiguous SPO loss function
9.1.7 The SPO+ loss function
9.1.8 Implementing the SPO+ loss function
9.2 An end-to-end SPO training procedure
9.2.1 End-to-end gradient descent
9.2.2 Preparing the modeling dataset
9.2.3 Preparing dataloaders
9.2.4 Preparing the neural network
9.2.5 Calculating regret as the optimality gap
9.2.6 Training a neural network with SPO+ loss
9.3 Summary