Nesterov momentum

Nesterov momentum, or Nesterov Acceleratedaccelerated Gradientgradient (NAG), is a slightly modified version of Momentummomentum with stronger theoretical convergence guarantees for convex functions. In practice, it has produced slightly better results than classical Momentummomentum. The gradient descent optimization algorithm follows the negative gradient of an objective function to locate its minimum. However, it has limitations, getting stuck in flat areas and struggling with noisy gradients. Momentum is an approach that accelerates the search, skimming across flat areas and smoothing noisy gradients. In some cases the acceleration of momentum causes the search to miss the minima. Nesterov momentum is a further extension that involves calculating the decaying moving average of the gradient for projected positions in the search space, not the actual positions themselves. This offers the benefits of momentum while reducing the chance of missing the minima.

Momentum is an approach that accelerates the search, skimming across flat areas and smoothing noisy gradients. In some cases, the acceleration of momentum causes the search to miss the minima. Nesterov momentum is a further extension that involves calculating the decaying moving average of the gradient for projected positions in the search space, not the actual positions themselves. This offers the benefits of momentum while reducing the chance of missing the minima.

Nesterov Momentummomentum was first described by Russian mathematician Yurii Nesterov in his 1983 paper titled “A Method For Solving The Convex Programming Problem With Convergence Rate O(1/k^2).” Neterov Momentummomentum was popularized by Ilya Sutskever, et al.al., applying the method to the training of neural networks with stochastic gradient descent. This work was described in their 2013 paper “On The Importance Of Initialization And Momentum In Deep Learning.”

In the standard Momentummomentum method, the gradient is computed using current parameters (θt). Nesterov momentum achieves stronger convergence by applying the velocity (vt) to the parameters in order to compute interim parameters (θ̃ = θt+μ*vt), where μ is the decay rate. These interim parameters are then used to compute the gradient, called a "lookahead" gradient step or a Nesterov Acceleratedaccelerated Gradientgradient.

The reason this is sometimes referred to as a "lookahead" gradient is that computing the gradient based on interim parameters allows NAG to change velocity in a faster and more responsive way, resulting in more stable behavior than classical Momentummomentum in many situations, particularly for higher values of μ. NAG is the correction factor for the classical Momentummomentum method.

Nesterov Momentummomentum can be described in terms of four steps:

Nesterov momentum improves the rate of convergence of the optimization algorithm (e.g.e.g., reduce the number of iterations required to find the solution), in particular in the field of convex optimization.

Nesterov momentum, or Nesterov Accelerated Gradient (NAG), is a slightly modified version of Momentum with stronger theoretical convergence guarantees for convex functions. In practice, it has produced slightly better results than classical Momentum.

Nesterov momentum, or Nesterov Accelerated Gradient (NAG), is a slightly modified version of Momentum with stronger theoretical convergence guarantees for convex functions. In practice, it has produced slightly better results than classical Momentum. The gradient descent optimization algorithm follows the negative gradient of an objective function to locate its minimum. However, it has limitations, getting stuck in flat areas and struggling with noisy gradients. Momentum is an approach that accelerates the search, skimming across flat areas and smoothing noisy gradients. In some cases the acceleration of momentum causes the search to miss the minima. Nesterov momentum is a further extension that involves calculating the decaying moving average of the gradient for projected positions in the search space, not the actual positions themselves. This offers the benefits of momentum while reducing the chance of missing the minima.

Nesterov Momentum was first described by Russian mathematician Yurii Nesterov in his 1983 paper titled “A Method For Solving The Convex Programming Problem With Convergence Rate O(1/k^2).” Neterov Momentum was popularized by Ilya Sutskever, et al. applying the method to the training of neural networks with stochastic gradient descent. This work was described in their 2013 paper “On The Importance Of Initialization And Momentum In Deep Learning.”

The reason this is sometimes referred to as a "lookahead" gradient is that computing the gradient based on interim parameters allowallows NAG to change velocity in a faster and more responsive way, resulting in more stable behavior than classical Momentum in many situations, particularly for higher values of μ. NAG is the correction factor for the classical Momentum method.

Nesterov Momentum can be described in terms of four steps:

1. Project the position of the solution
2. Calculate the gradient of the projection
3. Calculate the gradient of the projection
4. Update the variable

Nesterov momentum improves the rate of convergence of the optimization algorithm (e.g. reduce the number of iterations required to find the solution), in particular in the field of convex optimization.

Nesterov momentum, or Nesterov Accelerated Gradient (NAG), is a slightly modified version of Momentum with stronger theoretical convergence guarantees for convex functions. In practice, it has produced slightly better results than classical Momentum.

In the standard Momentum method, the gradient is computed using current parameters (θt). Nesterov momentum achieves stronger convergence by applying the velocity (vt) to the parameters in order to compute interim parameters (θ̃ = θt+μ*vt), where μ is the decay rate. These interim parameters are then used to compute the gradient, called a "lookahead" gradient step or a Nesterov Accelerated Gradient.

The reason this is sometimes referred to as a "lookahead" gradient is that computing the gradient based on interim parameters allow NAG to change velocity in a faster and more responsive way, resulting in more stable behavior than classical Momentum in many situations, particularly for higher values of μ. NAG is the correction factor for classical Momentum method.