Nesterov Accelerated Gradient is a type of optimization algorithm used in machine learning. It's based on stochastic gradient descent, which is a popular method for training neural networks. This optimizer uses momentum and looks ahead to where the parameters will be to calculate the gradient.
What is an Optimization Algorithm?
Before we talk about Nesterov Accelerated Gradient, let's first get an understanding of what an optimization algorithm is. In machine learning, an optimization algorithm is used to find the values of the parameters of a model that minimize the cost function. The cost function measures the difference between the predicted output of the model and the actual output. The goal of the optimization algorithm is to find the set of parameter values that result in the lowest possible cost.
The most common optimization algorithm used in machine learning is stochastic gradient descent (SGD). SGD works by updating the parameters of the model in small steps in the direction of the negative gradient of the cost function. The gradient is the vector of partial derivatives of the cost function with respect to each of the parameters.
What is Nesterov Accelerated Gradient?
Nesterov Accelerated Gradient is a modification of the standard SGD algorithm. It was proposed by Yurii Nesterov in 1983. The idea behind Nesterov Accelerated Gradient is to use momentum to speed up the convergence of the optimization algorithm. Momentum is a technique that helps the optimization algorithm to push through areas of shallow gradients and reach the global minimum faster.
The momentum term in Nesterov Accelerated Gradient is similar to the momentum term in SGD with momentum. However, in Nesterov Accelerated Gradient, the momentum term is used to update the gradient rather than the parameter values. The update equation for the momentum term is given as:
vt = γvt-1 + η∇θJ(θ-γvt-1)
where vt is the momentum term at time step t, γ is the momentum parameter (usually set to 0.9), η is the learning rate, ∇θJ(θ-γvt-1) is the gradient of the cost function with respect to the updated parameter values θ-γvt-1.
The updated parameter values are then calculated using the following equation:
θt = θt-1 + vt
where θt is the new parameter values at time step t, θt-1 is the previous parameter values, and vt is the momentum term at time step t.
Nesterov Accelerated Gradient vs Standard Momentum
The main difference between Nesterov Accelerated Gradient and standard momentum is the order in which the gradient is calculated. In standard momentum, the gradient is calculated at the current location and then a big jump is taken 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 intuition behind this is that it is better to correct a mistake after you have made it.
Nesterov Accelerated Gradient has been shown to converge faster than other optimization algorithms, especially when the cost function has a lot of shallow areas. In addition, it has been shown to be more robust to noise and can handle large-scale problems efficiently. However, it may not always be the best choice for all types of problems, and it's important to experiment with different optimization algorithms to find the one that works best for your specific problem.
Nesterov Accelerated Gradient is a momentum-based optimization algorithm that uses a look-ahead approach to calculate the gradient. It's a modification of the standard SGD algorithm and has been shown to be more efficient and robust in certain situations. Its use is becoming more and more prevalent in the field of machine learning, and it can be a powerful tool for improving the performance of your neural network models.
