CaVE: A Cone-Aligned Approach for Fast Predict-then-optimize with Binary Linear Programs
This work addresses the computational bottleneck in decision-focused learning for hard optimization problems like vehicle routing, offering a faster training method that is incremental but impactful for large-scale applications.
The paper tackles the challenge of training machine learning models in predict-then-optimize frameworks for binary linear programs by proposing CaVE, a method that aligns predicted cost vectors with normal cones to avoid solving BLPs during training, resulting in reduced training time while maintaining solution quality, as demonstrated in experiments including vehicle routing problems.
The end-to-end predict-then-optimize framework, also known as decision-focused learning, has gained popularity for its ability to integrate optimization into the training procedure of machine learning models that predict the unknown cost (objective function) coefficients of optimization problems from contextual instance information. Naturally, most of the problems of interest in this space can be cast as integer linear programs. In this work, we focus on binary linear programs (BLPs) and propose a new end-to-end training method to predict-then-optimize. Our method, Cone-aligned Vector Estimation (CaVE), aligns the predicted cost vectors with the normal cone corresponding to the true optimal solution of a training instance. When the predicted cost vector lies inside the cone, the optimal solution to the linear relaxation of the binary problem is optimal. This alignment not only produces decision-aware learning models but also dramatically reduces training time as it circumvents the need to solve BLPs to compute a loss function with its gradients. Experiments across multiple datasets show that our method exhibits a favorable trade-off between training time and solution quality, particularly with large-scale optimization problems such as vehicle routing, a hard BLP that has yet to benefit from predict-then-optimize methods in the literature due to its difficulty.