Optimization methods play a central role in signal processing, serving as the mathematical foundation for inference, estimation, and control. While classical iterative optimization algorithms provide interpretability and theoretical guarantees, they often rely on surrogate objectives, require careful hyperparameter tuning, and exhibit substantial computational latency. Conversely, machine learning (ML ) offers powerful data-driven modeling capabilities but lacks the structure, transparency, and efficiency needed for optimization-driven inference. Deep unfolding has recently emerged as a compelling framework that bridges these two paradigms by systematically transforming iterative optimization algorithms into structured, trainable ML architectures. This article provides a tutorial-style overview of deep unfolding, presenting a unified perspective of methodologies for converting optimization solvers into ML models and highlighting their conceptual, theoretical, and practical implications. We review the foundations of optimization for inference and for learning, introduce four representative design paradigms for deep unfolding, and discuss the distinctive training schemes that arise from their iterative nature. Furthermore, we survey recent theoretical advances that establish convergence and generalization guarantees for unfolded optimizers, and provide comparative qualitative and empirical studies illustrating their relative trade-offs in complexity, interpretability, and robustness.

翻译：优化方法在信号处理中占据核心地位，为推理、估计与控制提供了数学基础。经典的迭代优化算法虽具备可解释性与理论保证，但通常依赖于代理目标函数，需要精细的超参数调整，且存在显著的计算延迟。相比之下，机器学习（ML）虽具备强大的数据驱动建模能力，却缺乏优化驱动推理所需的结构化、透明性与效率。深度展开作为一种新兴框架，通过将迭代优化算法系统性地转化为结构化的可训练ML架构，有效连接了这两种范式。本文以教程形式综述深度展开方法，从统一视角阐述将优化求解器转化为ML模型的方法论，并着重探讨其概念、理论与实际意义。我们回顾了面向推理与学习的优化基础，介绍了四种具有代表性的深度展开设计范式，并讨论了由其迭代特性衍生的独特训练机制。此外，我们梳理了近期在理论层面的进展，这些研究为展开式优化器建立了收敛性与泛化性保证，并通过定性与实证对比研究，揭示了其在复杂度、可解释性与鲁棒性之间的权衡关系。