This paper presents a method for learning optimization algorithms by gradient descent, where the update rules of the optimizer are learned using recurrent neural networks (RNNs), specifically long short-term memory (LSTM) networks. The goal is to design an optimizer that can automatically learn to exploit the structure of the optimization problems it is trained on, and generalize to new tasks with similar structure. The proposed approach is tested on various tasks, including simple convex problems, training neural networks, and neural art style transfer. The key idea is to treat the design of an optimization algorithm as a learning problem, where the optimizer is modeled as a recurrent neural network that maintains its own state and dynamically updates based on the gradient information. The optimizer is trained to minimize the loss function by learning to adjust the parameters of the optimizee (the function to be optimized) based on the gradient of the function at each step. The paper demonstrates that the learned LSTM-based optimizer outperforms hand-designed competitors on the tasks for which they are trained, and also generalizes well to new tasks with similar structure. The approach is evaluated on several tasks, including training a neural network on the MNIST dataset, training a convolutional network on the CIFAR-10 dataset, and applying neural art style transfer. The results show that the learned optimizer significantly outperforms standard optimization methods in terms of convergence speed and performance on a variety of tasks. The paper also discusses the broader implications of this approach, showing that the learned optimizer can transfer knowledge between different problems, a concept known as transfer learning. This is particularly useful in scenarios where the optimizer is trained on a specific class of problems and needs to generalize to new tasks with similar structure. The results suggest that the learned optimizer can achieve significant improvements in performance, even when applied to tasks that are not directly related to the ones it was trained on.This paper presents a method for learning optimization algorithms by gradient descent, where the update rules of the optimizer are learned using recurrent neural networks (RNNs), specifically long short-term memory (LSTM) networks. The goal is to design an optimizer that can automatically learn to exploit the structure of the optimization problems it is trained on, and generalize to new tasks with similar structure. The proposed approach is tested on various tasks, including simple convex problems, training neural networks, and neural art style transfer. The key idea is to treat the design of an optimization algorithm as a learning problem, where the optimizer is modeled as a recurrent neural network that maintains its own state and dynamically updates based on the gradient information. The optimizer is trained to minimize the loss function by learning to adjust the parameters of the optimizee (the function to be optimized) based on the gradient of the function at each step. The paper demonstrates that the learned LSTM-based optimizer outperforms hand-designed competitors on the tasks for which they are trained, and also generalizes well to new tasks with similar structure. The approach is evaluated on several tasks, including training a neural network on the MNIST dataset, training a convolutional network on the CIFAR-10 dataset, and applying neural art style transfer. The results show that the learned optimizer significantly outperforms standard optimization methods in terms of convergence speed and performance on a variety of tasks. The paper also discusses the broader implications of this approach, showing that the learned optimizer can transfer knowledge between different problems, a concept known as transfer learning. This is particularly useful in scenarios where the optimizer is trained on a specific class of problems and needs to generalize to new tasks with similar structure. The results suggest that the learned optimizer can achieve significant improvements in performance, even when applied to tasks that are not directly related to the ones it was trained on.