Stochastic Optimization

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:

$$ v_{t} = \gamma{v}_{t-1} + \eta\nabla_{\theta}J\left(\theta-\gamma{v_{t-1}}\right) $$ $$\theta_{t} = \theta_{t-1} + v_{t}$$

Like SGD with momentum $\gamma$ is usually set to $0.9$.

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


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