  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. Finally, we show that the method is
applicable to several cases of smooth and non-smooth optimization and show
superior results to established accelerated solvers.
