LEAF: Learning-Enabled ADMM Framework Achieves Order-of-Magnitude Speedup in Convex Optimization
Researchers propose LEAF, a framework that combines machine learning with ADMM (Alternating Direction Method of Multipliers) optimization by using neural networks to approximate the Moreau envelope of objective functions. The approach uses Input Convex Neural Networks to preserve mathematical properties while reducing computational complexity. The method demonstrates significant speedups over existing solvers while maintaining theoretical convergence guarantees and low optimality gaps.
LEAF introduces a novel approach to accelerating convex optimization by learning a scalar-valued Moreau envelope approximation rather than learning high-dimensional operators directly. The framework consists of two variants—MEL-ADMM and sMEL-ADMM—both developed with rigorous theoretical analysis guaranteeing convergence and feasibility. By embedding convexity explicitly through the ICNN architecture, the method maintains high approximation accuracy while preserving the structural properties essential to optimization problems. The approach accommodates a broad class of convex problems with both smooth and non-smooth objectives. Numerical experiments show the framework achieves up to an order-of-magnitude speedup compared to state-of-the-art solvers while achieving convergence rates comparable to classical ADMM and maintaining low optimality gaps.
What's missing
The paper does not discuss computational requirements for training the neural network component, wall-clock time comparisons including training overhead, or applicability to non-convex problems. Specific benchmark problem classes and datasets used in experiments are not detailed in the abstract.
What different sources said
- arXiv cs.LGCenter
ML-Guided Primal Heuristics for Mixed Binary Quadratic Programs
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