Efficient differentiable quadratic programming layers: an ADMM approach

Recent advances in neural-network architecture allow for seamless integration of convex optimization problems as differentiable layers an end-to-end trainable neural network. Integrating medium and large scale quadratic programs into a deep network architecture, however, is challenging solving exactly by interior-point methods has worst-case cubic complexity the number variables. In this paper, we present alternative layer based on alternating direction method multipliers (ADMM) that capable scaling to moderate sized with 100–1000 decision variables thousands training examples. Backward differentiation performed implicit customized fixed-point iteration. Simulated results demonstrate computational advantage ADMM layer, which approximately order magnitude faster than state-of-the-art layers. Furthermore, our novel backward-pass routine computationally efficient comparison standard approach unrolled or KKT optimality conditions. We conclude examples from portfolio integrated prediction paradigm.