Learning to learn by gradient descent by gradient descent (1606.04474v2)

Abstract: The move from hand-designed features to learned features in machine learning has been wildly successful. In spite of this, optimization algorithms are still designed by hand. In this paper we show how the design of an optimization algorithm can be cast as a learning problem, allowing the algorithm to learn to exploit structure in the problems of interest in an automatic way. Our learned algorithms, implemented by LSTMs, outperform generic, hand-designed competitors on the tasks for which they are trained, and also generalize well to new tasks with similar structure. We demonstrate this on a number of tasks, including simple convex problems, training neural networks, and styling images with neural art.

• The paper introduces a novel LSTM-based optimizer that learns update rules by framing optimization as a meta-learning problem.
• The paper demonstrates through experiments that the learned optimizer outperforms traditional methods on tasks like MNIST and CIFAR-10.
• The paper highlights the potential for tailored and transferable optimization strategies, opening promising avenues for future research.

Learning to Learn by Gradient Descent by Gradient Descent

In the paper "Learning to learn by gradient descent by gradient descent," Andrychowicz et al. propose an innovative approach to optimization in machine learning, wherein the optimization algorithm itself is learned rather than hand-designed. This novel perspective leverages the principles of meta-learning to dynamically adapt optimization strategies using Long Short-Term Memory (LSTM) networks, demonstrating superior performance over traditional methods on various tasks.

Overview

The authors challenge the standard practice in machine learning of manually designing optimization algorithms, despite the successful transition from hand-designed features to learned features. They hypothesize that optimization can be formulated as a learning problem, where an optimizer, parameterized by a neural network (specifically an LSTM), learns to improve through gradient descent. Their learned optimizers, termed “LSTM optimizers,” demonstrated excellent performance and generalization capabilities on tasks including simple convex problems, training neural networks, and neural art styling.

Methodology

• Optimization as a Learning Problem: The paper casts the process of designing optimization algorithms as a learning problem. The meta-objective is to minimize the expected loss, defined over a distribution of optimization tasks, by learning the optimizer's parameters.
• LSTM-based Optimizer: The optimizer is modelled using a recurrent neural network (RNN), specifically an LSTM, which enables it to adapt and learn from the sequence of gradients over multiple steps. The parameter updates for the optimizee $\theta$ are given by:

$$\theta_{t+1} = \theta_t + g_t(\nabla f(\theta_t), \phi).$$

Here, $g_t$ is the learned update rule output by the LSTM $m$, parameterized by $\phi$.

Experiments and Results

The empirical evaluation was comprehensive, involving multiple tasks and demonstrating the robustness of the LSTM optimizers across different problem settings.

• Quadratic Functions: Testing on synthetic 10-dimensional quadratic functions revealed that LSTM optimizers outperformed traditional methods like SGD, RMSprop, and ADAM in terms of convergence speed and final loss.
• Training on MNIST: The trained LSTM optimizer significantly outperformed standard optimizers in training a simple neural network on the MNIST dataset. It also generalized well to variations in network architecture, such as different numbers of hidden units and layers.
• Convolutional Networks on CIFAR-10: When applied to a convolutional network for CIFAR-10 classification, LSTM optimizers showed superior performance in terms of both speed and accuracy compared to traditional optimizers. Remarkably, the learned optimizers transferred effectively to different subsets of CIFAR-10 and maintained performance even when applied to new data distributions.
• Neural Art: For the neural art styling task, the LSTM optimizer demonstrated robust performance across different styles and resolutions, adapting well to test scenarios significantly different from the training settings.

Implications and Future Directions

The idea of learning to optimize offers significant practical and theoretical implications:

• Tailored Optimization: Optimizers can be specialized to particular classes of problems, leading to enhanced performance in those contexts.
• Generalization: The ability of learned optimizers to generalize across related tasks and architectures can streamline the training of complex models.
• Meta-Learning: By viewing optimization as a learning problem, this work bridges the gap between meta-learning and traditional optimization, suggesting numerous avenues for future research in creating more sophisticated and adaptive learning algorithms.

Conclusion

Andrychowicz et al. successfully establish that optimization algorithms need not be hand-designed but can be dynamically learned, leveraging the power of LSTMs. This paradigm shift holds promise for a wide range of machine learning applications, potentially leading to more efficient and robust optimization techniques tailored to specific problem domains. Future work might explore extending these ideas to other neural network architectures and more complex, real-world tasks, refining the robustness and adaptability of learned optimizers.