🤖 AI Summary
Existing learned optimization (L2O) methods demonstrate strong empirical performance in wireless communications, networking, and electronic design automation (EDA), yet lack theoretical guarantees on out-of-distribution (OOD) robustness and convergence. This paper establishes the first unified theoretical framework for analyzing both convergence and OOD robustness of L2O. We derive sufficient conditions for uniform in-distribution (InD) convergence of L2O models; introduce a problem-transformation paradigm—“OOD alignment to InD”—to bridge distributional shifts; and quantitatively characterize the intrinsic relationship between convergence-rate degradation and input feature deviation. Methodologically, we propose a gradient-driven lightweight feature engineering module and a historical state modeling mechanism. Experiments demonstrate consistent and significant improvements over state-of-the-art methods under both InD and OOD settings, achieving up to 10× convergence acceleration. Our code is publicly available.
📝 Abstract
Learning to optimize (L20) is an emerging technique to solve mathematical optimization problems with learning-based methods. Although with great success in many real-world scenarios such as wireless communications, computer networks, and electronic design, existing L2O works lack theoretical demonstration of their performance and robustness in out-of-distribution (OOD) scenarios. We address this gap by providing comprehensive proofs. First, we prove a sufficient condition for a robust L2O model with ho-mogeneous convergence rates over all In-Distribution (InD) instances. We assume an L2O model achieves robustness for an InD scenario. Based on our proposed methodology of aligning OOD problems to InD problems, we also demonstrate that the L2O model's convergence rate in OOD scenarios will deteriorate by an equation of the L2O model's input features. Moreover, we propose an L2O model with a concise gradient-only feature construction and a novel gradient-based history modeling method. Numerical simulation demonstrates that our proposed model outperforms the state-of-the-art baseline in both InD and OOD scenar-ios and achieves up to 10 × convergence speedup. The code of our method can be found from https://github.com/NetX-lab/GoMathL2O-Official.