Nesterov Accelerated Gradient

Nesterov Accelerated Gradient is a momentum-based SGD optimizer that "looks ahead" to where the parameters will be to calculate the gradient ex post rather than ex ante:

$v\_{t} = \gamma{v}\_{t-1} - \eta\nabla\_{\theta}J\left(\theta_{t-1}+\gamma{v\_{t-1}}\right)$ $\theta\_{t} = \theta\_{t-1} + v\_{t}$ $\gamma, \eta \in \mathbb{R}^+$

Like SGD with momentum $\gamma$ is usually set to $0.9$. $\eta$ and $\gamma$ are usually less than $1$.

The intuition is that the standard momentum method first computes the gradient at the current location and then takes a big jump in the direction of the updated accumulated gradient. In contrast Nesterov momentum first makes a big jump in the direction of the previous accumulated gradient and then measures the gradient where it ends up and makes a correction. The idea being that it is better to correct a mistake after you have made it.

Image Source: Geoff Hinton lecture notes