Central Path SPO: An Interior-Projection Based Approach for Solver-Free Decision-Focused Learning

Decision-focused learning trains predictive models for the quality of the decisions they induce, but repeated optimization during training limits its scalability. By leveraging concepts from path-following methods in convex programming, and recent advances in constrained machine learning, we formulate a novel framework for solver-free decision-focused learning for linear programs. The framework is based on training a neural network to directly learn the solution of a much easier, smoothed and regularized version of the linear program via first-order methods and an interior projection map. Via Fenchel conjugacy, the learned smooth solution is transformed into a cost prediction, which is used to solve the original linear program at inference. The framework is applicable with any suitably chosen interior projection map and legendre function regularizer. We focus on the case where the interior projection map is a soft-radial projection anchored to the analytic center of the constraint set, and the regularizer is a logarithmic barrier from the classical theory of interior point methods. The resulting method is both fast, and highly performant. We derive theoretical guarantees, and evaluate the method on large scale versions of standard benchmarks, achieving lower regret and order-of- magnitude speed-ups compared with standard approaches.