Training Deep Neural Networks with Adaptive Momentum Inspired by the Quadratic Optimization

TL;DR

This paper introduces an adaptive momentum method inspired by quadratic optimization to enhance stochastic gradient methods, reducing hyperparameter tuning and improving convergence, robustness, and generalization across various machine learning tasks.

Contribution

The paper proposes a novel adaptive momentum scheme for SGD and Adam, eliminating the need for hyperparameter tuning and providing theoretical convergence guarantees.

Findings

Improved convergence speed of SGD and Adam with adaptive momentum

Enhanced robustness to large learning rates

Better generalization performance on diverse benchmarks

Abstract

Heavy ball momentum is crucial in accelerating (stochastic) gradient-based optimization algorithms for machine learning. Existing heavy ball momentum is usually weighted by a uniform hyperparameter, which relies on excessive tuning. Moreover, the calibrated fixed hyperparameter may not lead to optimal performance. In this paper, to eliminate the effort for tuning the momentum-related hyperparameter, we propose a new adaptive momentum inspired by the optimal choice of the heavy ball momentum for quadratic optimization. Our proposed adaptive heavy ball momentum can improve stochastic gradient descent (SGD) and Adam. SGD and Adam with the newly designed adaptive momentum are more robust to large learning rates, converge faster, and generalize better than the baselines. We verify the efficiency of SGD and Adam with the new adaptive momentum on extensive machine learning benchmarks, including image classification, language modeling, and machine translation. Finally, we provide convergence guarantees for SGD and Adam with the proposed adaptive momentum.