Learning Gradients of Convex Functions with Monotone Gradient Networks

However, it is often a laborious process that involves While much effort has been devoted to deriving and analyzing manually designing suitable convex objectives and associated effective convex formulations of signal processing problems, convex constraints. Perhaps more important than the the gradients of convex functions also have critical applications objective function itself is the gradient of the function, since ranging from gradient-based optimization to optimal most convex problems are solved using computationally frugal transport. Recent works have explored data-driven methods gradient-based methods. Monotone gradient maps of convex for learning convex objective functions, but learning their functions also have critical applications in domains including monotone gradients is seldom studied. In this work, we propose gradient-based optimization, generalized linear models, C-MGN and M-MGN, two monotone gradient neural network linear inverse problems, and optimal transport. Therefore, architectures for directly learning the gradients of convex in this work, we propose to learn the gradient of convex functions. We show that, compared to state of the art functions in a data-driven manner using deep learning. Our methods, our networks are easier to train, learn monotone approach is a fundamental step toward blending strengths of gradient fields more accurately, and use significantly fewer both deep learning and convex optimization and offers a wide parameters. We further demonstrate their ability to learn optimal array of applications in data science and signal processing.