Predict+Optimise with Ranking Objectives: Exhaustively Learning Linear Functions

We study the predict+optimise problem, where machine learning and combinatorial optimisation must interact to achieve a common goal. These problems are important when optimisation needs to be performed on input parameters that are not fully observed but must instead be estimated using machine learning. Our contributions are two-fold: 1) we provide theoretical insight into the properties and computational complexity of predict+optimise problems in general, and 2) develop a novel framework that, in contrast to related work, guarantees to compute the optimal parameters for a linear learning function given any ranking optimisation problem. We illustrate the applicability of our framework for the particular case of the unit-weighted knapsack predict+optimise problem and evaluate on benchmarks from the literature.