In recent years, deep learning has achieved remarkable success in various fields such as image recognition, natural language processing, and speech recognition. The effectiveness of deep learning largely depends on the optimization methods used to train deep neural networks. In this paper, we provide an overview of first-order optimization methods such as Stochastic Gradient Descent, Adagrad, Adadelta, and RMSprop, as well as recent momentum-based and adaptive gradient methods such as Nesterov accelerated gradient, Adam, Nadam, AdaMax, and AMSGrad. We also discuss the challenges associated with optimization in deep learning and explore techniques for addressing these challenges, including weight initialization, batch normalization, and layer normalization. Finally, we provide recommendations for selecting optimization methods for different deep learning tasks and datasets. This paper serves as a comprehensive guide to optimization methods in deep learning and can be used as a reference for researchers and practitioners in the field.

翻译：近年来，深度学习在图像识别、自然语言处理和语音识别等多个领域取得了显著成功。深度学习的有效性在很大程度上取决于用于训练深度神经网络的优化方法。本文概述了随机梯度下降、Adagrad、Adadelta和RMSprop等一阶优化方法，以及近期基于动量和自适应梯度的方法，如Nesterov加速梯度、Adam、Nadam、AdaMax和AMSGrad。我们还讨论了深度学习中优化面临的挑战，并探讨了应对这些挑战的技术，包括权重初始化、批量归一化和层归一化。最后，我们针对不同深度学习任务和数据集提出了选择优化方法的建议。本文可作为深度学习优化方法的综合指南，为该领域的研究人员和实践者提供参考。