CaVE: A Cone-Aligned Approach for Fast Predict-then-optimize with Binary Linear Programs
arxiv(2023)
摘要
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.
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