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arXiv · 1904.09043

Differentiating Through a Cone Program

Akshay Agrawal·Shane Barratt·Stephen Boyd·Enzo Busseti·Walaa M. Moursi
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Abstract

We consider the problem of efficiently computing the derivative of the solution map of a convex cone program, when it exists. We do this by implicitly differentiating the residual map for its homogeneous self-dual embedding, and solving the linear systems of equations required using an iterative method. This allows us to efficiently compute the derivative operator, and its adjoint, evaluated at a vector. These correspond to computing an approximate new solution, given a perturbation to the cone program coefficients (i.e., perturbation analysis), and to computing the gradient of a function of the solution with respect to the coefficients. Our method scales to large problems, with numbers of coefficients in the millions. We present an open-source Python implementation of our method that solves a cone program and returns the derivative and its adjoint as abstract linear maps; our implementation can be easily integrated into software systems for automatic differentiation.

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Akshay Agrawal, Shane Barratt, Stephen Boyd, Enzo Busseti, Walaa M. Moursi. 2019-04-19. Differentiating Through a Cone Program. https://arxiv.org/abs/1904.09043

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