Accelerated Forward-Backward Optimization Using Deep Learning

.We propose several deep-learning accelerated optimization solvers with convergence guarantees. We use ideas from the analysis of accelerated forward-backward schemes like FISTA, but instead of the classical approach of proving convergence for a choice of parameters, such as a step-size, we show convergence whenever the update is chosen in a specific set. Rather than picking a point in this set using some predefined method, we train a deep neural network to pick the best update within a given space. Finally, we show that the method is applicable to several cases of smooth and nonsmooth optimization and show superior results to established accelerated solvers.Keywordsconvex optimizationdeep learningproximal-gradient algorithminverse problemsMSC codes90C2590C0668T0749M3765K10