A Mathematics-Inspired Learning-to-Optimize Framework for Decentralized Optimization
Keywords: Learning to Optimize, Decentralized Optimization, Composite Optimization
TL;DR: This paper proposes MiLoDo, a learned algorithm for decentralized optimization with impressive generalization abilities.
Abstract: 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 the necessary conditions that successful decentralized algorithmic rules need to satisfy to achieve both optimality and consensus. Based on these conditions, we propose a novel **M**athematics-**i**nspired **L**earning-to-**o**ptimize framework for **D**ecentralized **o**ptimization (**MiLoDo**). 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.
Primary Area: optimization
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Submission Number: 5439
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