# Safeguarded Learned Convex Optimization

arXiv: https://arxiv.org/abs/2003.01880 · HTML: https://mlsanity.com/paper/2003.01880/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Mar 2020.

## Built on by (most cited first, 24 of 24)

- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Learning to Warm-Start Fixed-Point Optimization Algorithms](https://mlsanity.com/paper/2309.07835/) (2023)
- [A Simple Guard for Learned Optimizers](https://mlsanity.com/paper/2201.12426/) (2022)
- [Robust Stochastically-Descending Unrolled Networks](https://mlsanity.com/paper/2312.15788/) (2023)
- [Curvature-Aware Derivative-Free Optimization](https://mlsanity.com/paper/2109.13391/) (2021)
- [Learning to optimize with convergence guarantees using nonlinear system theory](https://mlsanity.com/paper/2403.09389/) (2024)
- [Deep Unfolding: Recent Developments, Theory, and Design Guidelines](https://mlsanity.com/paper/2512.03768/) (2025)
- [Stochastic Unrolled Federated Learning](https://mlsanity.com/paper/2305.15371/) (2023)
- [Optimization-Derived Learning with Essential Convergence Analysis of Training and Hyper-training](https://mlsanity.com/paper/2206.07875/) (2022)
- [Learning to Optimize with Dynamic Mode Decomposition](https://mlsanity.com/paper/2211.16268/) (2022)
- [Data-Driven Performance Guarantees for Classical and Learned Optimizers](https://mlsanity.com/paper/2404.13831/) (2024)
- [M-L2O: Towards Generalizable Learning-to-Optimize by Test-Time Fast Self-Adaptation](https://mlsanity.com/paper/2303.00039/) (2023)
- [Robustified Learning for Online Optimization with Memory Costs](https://mlsanity.com/paper/2305.00677/) (2023)
- [Deep FlexQP: Accelerated Nonlinear Programming via Deep Unfolding](https://mlsanity.com/paper/2512.01565/) (2025)
- [Hierarchical Optimization-Derived Learning](https://mlsanity.com/paper/2302.05587/) (2023)
- [Learning to optimize with guarantees: a complete characterization of linearly convergent algorithms](https://mlsanity.com/paper/2508.00775/) (2025)
- [From Learning to Optimize to Learning Optimization Algorithms](https://mlsanity.com/paper/2405.18222/) (2024)
- [Learning to accelerate Krasnosel'skii-Mann fixed-point iterations with guarantees](https://mlsanity.com/paper/2601.07665/) (2026)
- [A Design Space Study for LISTA and Beyond](https://mlsanity.com/paper/2104.04110/) (2021)
- [A Generalization Result for Convergence in Learning-to-Optimize](https://mlsanity.com/paper/2410.07704/) (2024)
- [Physics-Inspired Binary Neural Networks: Interpretable Compression with Theoretical Guarantees](https://mlsanity.com/paper/2502.01908/) (2025)
- [Learning to optimize by multi-gradient for multi-objective optimization](https://mlsanity.com/paper/2311.00559/) (2023)
- [Learning Provably Improves the Convergence of Gradient Descent](https://mlsanity.com/paper/2501.18092/) (2025)
- [Towards Robust Learning to Optimize with Theoretical Guarantees](https://mlsanity.com/paper/2506.14263/) (2025)

## Abstract (arXiv)

Applications abound in which optimization problems must be repeatedly solved, each time with new (but similar) data. Analytic optimization algorithms can be hand-designed to provably solve these problems in an iterative fashion. On one hand, data-driven algorithms can "learn to optimize" (L2O) with much fewer iterations and similar cost per iteration as general-purpose optimization algorithms. On the other hand, unfortunately, many L2O algorithms lack converge guarantees. To fuse the advantages of these approaches, we present a Safe-L2O framework. Safe-L2O updates incorporate a safeguard to guarantee convergence for convex problems with proximal and/or gradient oracles. The safeguard is simple and computationally cheap to implement, and it is activated only when the data-driven L2O updates would perform poorly or appear to diverge. This yields the numerical benefits of employing machine learning to create rapid L2O algorithms while still guaranteeing convergence. Our numerical examples show convergence of Safe-L2O algorithms, even when the provided data is not from the distribution of training data.