Lookahead Optimizer: k steps forward, 1 step back (1907.08610v2)

Abstract: The vast majority of successful deep neural networks are trained using variants of stochastic gradient descent (SGD) algorithms. Recent attempts to improve SGD can be broadly categorized into two approaches: (1) adaptive learning rate schemes, such as AdaGrad and Adam, and (2) accelerated schemes, such as heavy-ball and Nesterov momentum. In this paper, we propose a new optimization algorithm, Lookahead, that is orthogonal to these previous approaches and iteratively updates two sets of weights. Intuitively, the algorithm chooses a search direction by looking ahead at the sequence of fast weights generated by another optimizer. We show that Lookahead improves the learning stability and lowers the variance of its inner optimizer with negligible computation and memory cost. We empirically demonstrate Lookahead can significantly improve the performance of SGD and Adam, even with their default hyperparameter settings on ImageNet, CIFAR-10/100, neural machine translation, and Penn Treebank.

• The paper introduces a dual weight update strategy that reduces variance and enhances convergence by combining fast and slow weights.
• Experiments on CIFAR, ImageNet, and language models demonstrate faster convergence and robust performance with minimal hyperparameter tuning.
• Theoretical analysis reveals lower variance steady states and improved efficiency over traditional SGD-based methods.

Overview of Lookahead Optimizer: $k$ Steps Forward, 1 Step Back

The paper "Lookahead Optimizer: $k$ Steps Forward, 1 Step Back" introduces an innovative optimization algorithm, Lookahead, that deviates from traditional approaches like adaptive learning rate schemes and accelerated methods. This optimizer operates by iteratively updating two sets of weights, fast and slow, where the fast weights are generated by a standard optimizer, and the slow weights provide updates converging toward the fast weights.

Core Contributions

Lookahead is proposed as orthogonal to existing SGD improvements, focusing on reducing variance, enhancing learning stability, and diminishing the need for extensive hyperparameter tuning. Rather than improving adaptive or accelerated schemes, Lookahead adds a novel dimension where the search direction is determined by inspecting the trajectory of fast weights.

Empirical Results and Analysis

Significant improvements are demonstrated when Lookahead is applied to tasks such as image classification using ResNet architectures on CIFAR-10/100 and ImageNet, neural machine translation, and LSTM LLMs on the Penn Treebank dataset. It achieves faster convergence and better generalization compared to its inner optimizers, such as SGD and Adam, while displaying robustness to hyperparameter variations.

Numerical results highlight the robustness and efficiency of Lookahead:

• CIFAR and ImageNet: Lookahead enhances convergence speed and achieves comparable or superior accuracy with negligible computational overhead.
• LLMing and NMT: On Penn Treebank, it outperforms both SGD and Adam, while for Transformers, it facilitates faster early-stage convergence.

Theoretical Implications

The paper provides a theoretical convergence analysis, illustrating how Lookahead reduces variance in optimization tasks. The steady-state analysis on a noisy quadratic model shows Lookahead maintaining a smaller variance fixed point compared to SGD. For deterministic quadratic functions, Lookahead demonstrates improved convergence in under-damped regimes.

Computational Complexity and Robustness

Lookahead incurs only a constant computational overhead, proportional to the number of inner updates. Its resilience to suboptimal learning rates, momentum settings, and insensitivity to hyperparameters ($\alpha$ and $k$) in practical experiments, showcase its robustness.

Future Directions

This research opens avenues for further exploration, including integration with other advanced optimization algorithms or learning rate schedules and extending Lookahead's applicability to broader AI domains. The adaptability of Lookahead to different inner optimizers and conditions posits it as a promising tool for dynamic environments and complex model training, albeit requiring careful implementation tuning.

Overall, the paper methodically outlines a new pathway for optimization in neural networks, substantiated by strong empirical results and thorough analysis.