DeepAI

# Time-Delay Momentum: A Regularization Perspective on the Convergence and Generalization of Stochastic Momentum for Deep Learning

In this paper we study the problem of convergence and generalization error bound of stochastic momentum for deep learning from the perspective of regularization. To do so, we first interpret momentum as solving an ℓ_2-regularized minimization problem to learn the offsets between arbitrary two successive model parameters. We call this time-delay momentum because the model parameter is updated after a few iterations towards finding the minimizer. We then propose our learning algorithm, stochastic gradient descent (SGD) with time-delay momentum. We show that our algorithm can be interpreted as solving a sequence of strongly convex optimization problems using SGD. We prove that under mild conditions our algorithm can converge to a stationary point with rate of O(1/√(K)) and generalization error bound of O(1/√(nδ)) with probability at least 1-δ, where K,n are the numbers of model updates and training samples, respectively. We demonstrate the empirical superiority of our algorithm in deep learning in comparison with the state-of-the-art deep learning solvers.

• 47 publications
• 11 publications
• 10 publications
02/24/2020

### Scheduled Restart Momentum for Accelerated Stochastic Gradient Descent

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### Escaping Saddle Points Faster with Stochastic Momentum

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### Robust Sampling in Deep Learning

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### Positive-Negative Momentum: Manipulating Stochastic Gradient Noise to Improve Generalization

It is well-known that stochastic gradient noise (SGN) acts as implicit r...
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### Momentum in Reinforcement Learning

We adapt the optimization's concept of momentum to reinforcement learnin...
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### DEAM: Accumulated Momentum with Discriminative Weight for Stochastic Optimization

Optimization algorithms with momentum, e.g., Nesterov Accelerated Gradie...
05/31/2016

### Asynchrony begets Momentum, with an Application to Deep Learning

Asynchronous methods are widely used in deep learning, but have limited ...