# Accelerated Forward-Backward Optimization using Deep Learning

arXiv: https://arxiv.org/abs/2105.05210 · HTML: https://mlsanity.com/paper/2105.05210/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 May 2021.

## Built on by (most cited first, 11 of 11)

- [Learned reconstruction methods with convergence guarantees](https://mlsanity.com/paper/2206.05431/) (2022)
- [Learning to Warm-Start Fixed-Point Optimization Algorithms](https://mlsanity.com/paper/2309.07835/) (2023)
- [Neural incomplete factorization: learning preconditioners for the conjugate gradient method](https://mlsanity.com/paper/2305.16368/) (2023)
- [Data-Driven Performance Guarantees for Classical and Learned Optimizers](https://mlsanity.com/paper/2404.13831/) (2024)
- [ODE-based Learning to Optimize](https://mlsanity.com/paper/2406.02006/) (2024)
- [Deep FlexQP: Accelerated Nonlinear Programming via Deep Unfolding](https://mlsanity.com/paper/2512.01565/) (2025)
- [Learning to optimize with guarantees: a complete characterization of linearly convergent algorithms](https://mlsanity.com/paper/2508.00775/) (2025)
- [Learning to accelerate distributed ADMM using graph neural networks](https://mlsanity.com/paper/2509.05288/) (2025)
- [Warm-starting active-set solvers using graph neural networks](https://mlsanity.com/paper/2511.13174/) (2025)
- [Learning to accelerate Krasnosel'skii-Mann fixed-point iterations with guarantees](https://mlsanity.com/paper/2601.07665/) (2026)
- [Deep learning based dictionary learning and tomographic image reconstruction](https://mlsanity.com/paper/2108.11730/) (2021)

## Abstract (arXiv)

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.