liikemääräohjaimia

Liikemääräohjaimia, or momentum controllers, are a class of algorithms used in machine learning, particularly in training artificial neural networks. They aim to accelerate the convergence of the training process and help overcome issues like vanishing or exploding gradients. The core idea behind momentum is to introduce a fraction of the previous update vector into the current update. This helps the optimizer "roll down" the cost function landscape more smoothly, similar to a ball rolling down a hill.

The standard momentum method, often referred to as "heavy ball" momentum, adds a term proportional to the previous weight update to the current gradient descent update. Mathematically, this can be expressed as:

v_t = gamma * v_{t-1} + eta * nabla_theta J(theta_t)

theta_{t+1} = theta_t - v_t

where v_t is the update vector at time t, gamma is the momentum coefficient (typically between 0 and 1), eta is the learning rate, and nabla_theta J(theta_t) is the gradient of the cost function J with respect to the parameters theta at time t.

Another popular variant is Nesterov Accelerated Gradient (NAG). NAG modifies the standard momentum approach by calculating the gradient not at the current parameter position, but at a position slightly ahead in the direction of the previous update. This "lookahead" mechanism can provide a more responsive update and often leads to better performance. The update rule for NAG is slightly different, involving computing the gradient after a "lookahead" step.

Liikemääräohjaimia are effective in situations where the cost function has shallow gradients or is noisy. By accumulating information from past gradients, they can help the optimizer maintain a consistent direction and avoid oscillations. This can lead to faster convergence and the ability to escape shallow local minima.