LEAF: A Learning-Enabled ADMM Framework for Accelerated Convex Optimization
2026-06-08 • Machine Learning
Machine Learning
AI summaryⓘ
The authors introduce LEAF, a new method that speeds up solving certain math problems called convex optimization. They use a special neural network to learn a simpler version of the problem, making it easier and faster to solve. This approach keeps important math properties intact, ensuring reliable results. Their method matches traditional solvers in accuracy but runs faster, as shown in their experiments.
Convex optimizationADMM (Alternating Direction Method of Multipliers)Moreau envelopeInput Convex Neural Network (ICNN)ConvergenceSmooth and non-smooth objectivesModel complexityData efficiency
Authors
Binh Nguyen, Trinh Tran, Truong X. Nghiem
Abstract
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