The main idea of Nesterov accelerated gradient (NAG, Nesterov momentum) is to update the parameter with the gradient at the predicted (peeked-ahead) parameter. To reduce the sample variance, NAG smoothes the update by exponentially averaging the histories.

Sutskever et al.[1] proved that NAG was effective to improve the stability and convergence rate of stochastic optimization of deep network. They showed it could be done in two steps.

Simplified Nesterov momentum updates:

Bengio et al.[2] reformulated it to indicate that it was equivalent to the standard momentum except for different linear weighting coefficients.

[1] Sutskever, I., Martens, J., Dahl, G. and Hinton, G. E. On the importance of momentum and initialization in deep learning. In 30th International Conference on Machine Learning, Atlanta, USA, 2013. JMLR: W&CP volume 28.
[2] Yoshua Bengio, Nicolas Boulanger-Lewandowski, Razvan Pascanu. Advances in Optimizing Recurrent Networks. arXiv 1212.0901.