2026 Xu Differentiable Optimization Power Systems

Decision-focused learning (DfL) trains forecasting models to align downstream decision consequences, such as power-system operating costs. However, its application to realistic power networks is hindered by the requirement to repeatedly solve and differentiate large optimization problems during training. This paper introduces DiffAPQP, a solver-flexible framework and open-source Python package designed for scalable DfL using affine-parametric quadratic programs. The methodology involves automatically canonicalizing quadratic power-system models written in CVXPY into a differentiation-ready form, utilizing solver warm-starts and data updates to accelerate training. Notably, we've established that differentiation via the full KKT system can be efficiently achieved through a reduced system by eliminating inactive inequality constraints. Moreover, for training losses reliant on optimal values, we derived an envelope-theorem-based gradient, thereby avoiding the need to solve an adjoint KKT system, which reduces backward processing time. This work marks the first solver-based end-to-end DfL demonstration on the IEEE 118-bus system with a 24-hour economic-dispatch and redispatch scenario. Experimental results indicate that DiffAPQP can achieve closed-loop speedups ranging from 2.27× to 3.58× compared to CvxpyLayers, with significant reductions in peak memory usage while maintaining comparable operating costs.