# LEAF: A Learning-Enabled ADMM Framework for Accelerated Convex Optimization

arXiv: https://arxiv.org/abs/2606.08993 · HTML: https://mlsanity.com/paper/2606.08993/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 49 references that are in the map.
- First posted on arXiv 8 Jun 2026.

## Builds on (most cited first, 26 of 26)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (2019)
- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [OSQP: An Operator Splitting Solver for Quadratic Programs](https://mlsanity.com/paper/1711.08013/) (2017)
- [Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problems](https://mlsanity.com/paper/1704.03488/) (2017)
- [Learning Optimal Solutions for Extremely Fast AC Optimal Power Flow](https://mlsanity.com/paper/1910.01213/) (2019)
- [One Network to Solve Them All --- Solving Linear Inverse Problems using Deep Projection Models](https://mlsanity.com/paper/1703.09912/) (2017)
- [Self-Supervised Primal-Dual Learning for Constrained Optimization](https://mlsanity.com/paper/2208.09046/) (2022)
- [Clarabel: An interior-point solver for conic programs with quadratic objectives](https://mlsanity.com/paper/2405.12762/) (2024)
- [Learning for Constrained Optimization: Identifying Optimal Active Constraint Sets](https://mlsanity.com/paper/1802.09639/) (2018)
- [Learning Warm-Start Points for AC Optimal Power Flow](https://mlsanity.com/paper/1905.08860/) (2019)
- [Learning to Warm-Start Fixed-Point Optimization Algorithms](https://mlsanity.com/paper/2309.07835/) (2023)
- [HardNet: Hard-Constrained Neural Networks with Universal Approximation Guarantees](https://mlsanity.com/paper/2410.10807/) (2024)
- [A General Analysis of the Convergence of ADMM](https://mlsanity.com/paper/1502.02009/) (2015)
- [FSNet: Feasibility-Seeking Neural Network for Constrained Optimization with Guarantees](https://mlsanity.com/paper/2506.00362/) (2025)
- [Learning to Optimize in Model Predictive Control](https://mlsanity.com/paper/2212.02603/) (2022)
- [Strongly convex functions, Moreau envelopes and the generic nature of convex functions with strong minimizers](https://mlsanity.com/paper/1507.07144/) (2015)
- [QC-ODKLA: Quantized and Communication-Censored Online Decentralized Kernel Learning via Linearized ADMM](https://mlsanity.com/paper/2208.02777/) (2022)
- [GPU-accelerated dynamic nonlinear optimization with ExaModels and MadNLP](https://mlsanity.com/paper/2403.15913/) (2024)
- [Economic MPC with an Online Reference Trajectory for Battery Scheduling Considering Demand Charge Management](https://mlsanity.com/paper/2412.10851/) (2024)
- [KKT-based optimality conditions for neural network approximation](https://mlsanity.com/paper/2506.17305/) (2025)

## Built on by (most cited first, 1 of 1)

- [Learning-enabled Acceleration of Scenario-based Model Predictive Control](https://mlsanity.com/paper/2607.12775/) (2026)

## Abstract (arXiv)

We propose LEAF, a learning-enabled ADMM framework for accelerated convex optimization. The key idea is to approximate the Moreau envelope of the objective function using an Input Convex Neural Network (ICNN), resulting in a learned model that preserves convexity and smoothness. This leads to the proposed Moreau Envelope Learning ADMM (MEL-ADMM) and its splitting variant sMEL-ADMM. Unlike existing approaches that learn high-dimensional operators directly, LEAF learns a scalar-valued Moreau envelope, significantly reducing model complexity and improving data efficiency. The framework accommodates a broad class of convex problems with smooth and non-smooth objectives. By embedding convexity explicitly through the ICNN architecture, the proposed approach maintains high approximation accuracy while preserving key structural properties of the optimization problem. Both MEL-ADMM and sMEL-ADMM are developed with theoretical guarantees of convergence and feasibility under the learned model. Rigorous analysis shows that the proposed methods achieve convergence rates comparable to classical ADMM while reducing per-iteration computational cost. Numerical experiments demonstrate up to an order-of-magnitude speedup over state-of-the-art solvers while maintaining low optimality gaps