9 Regularization via Smart Predict-then-Optimize

 

This chapter covers

  • 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