A Convergence-Motivated Learning-to-Optimize Framework for Decentralized Optimization

Yutong He

doi:10.1109/TSP.2025.3644008

A Convergence-Motivated Learning-to-Optimize Framework for Decentralized Optimization

2025-12-15

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DOI：10.1109/TSP.2025.3644008

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Most decentralized optimization algorithms are handcrafted. While endowed with strong theoretical guarantees, these algorithms generally target a broad class of problems, thereby not being adaptive or customized to specific problem features. This paper studies data-driven decentralized algorithms trained to exploit problem features to boost convergence. Existing learning-to-optimize methods typically suffer from poor generalization or prohibitively vast search spaces. In addition, they face more challenges in decentralized settings where nodes must reach consensus through neighborhood communications without global information. To resolve these challenges, this paper first derives necessary conditions for decentralized algorithmic rules to achieve both optimality and consensus. Then, we propose a novel Convergence-<bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Motivated Learning-to-optimize framework for Decentralized optimization (MiLoDo) based on these conditions. Empirical results demonstrate that MiLoDo-trained algorithms outperform handcrafted algorithms and exhibit strong generalizations. Algorithms learned via MiLoDo in 100 iterations perform robustly when running 100,000 iterations during inferences. Moreover, MiLoDo-trained algorithms on synthetic datasets perform well on problems involving real data, higher dimensions, and different loss functions. Codes are available at: <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/pkumelon/MiLoDo</uri>.

Keywords:

Decentralized optimization

learning-to-optimize

generic L2O

non-smooth optimization

A Convergence-Motivated Learning-to-Optimize Framework for Decentralized Optimization

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