Learning rate

Optimization algorithms and methods | Model selection

In machine learning and statistics, the learning rate is a tuning parameter in an optimization algorithm that determines the step size at each iteration while moving toward a minimum of a loss function. Since it influences to what extent newly acquired information overrides old information, it metaphorically represents the speed at which a machine learning model "learns". In the adaptive control literature, the learning rate is commonly referred to as gain. In setting a learning rate, there is a trade-off between the rate of convergence and overshooting. While the descent direction is usually determined from the gradient of the loss function, the learning rate determines how big a step is taken in that direction. A too high learning rate will make the learning jump over minima but a too low learning rate will either take too long to converge or get stuck in an undesirable local minimum. In order to achieve faster convergence, prevent oscillations and getting stuck in undesirable local minima the learning rate is often varied during training either in accordance to a learning rate schedule or by using an adaptive learning rate. The learning rate and its adjustments may also differ per parameter, in which case it is a diagonal matrix that can be interpreted as an approximation to the inverse of the Hessian matrix in Newton's method. The learning rate is related to the step length determined by inexact line search in quasi-Newton methods and related optimization algorithms. When conducting line searches, mini-batch sub-sampling (MBSS) affect the characteristics of the loss function along which the learning rate needs to be resolved. Static MBSS keeps the mini-batch fixed along a search direction, resulting in a smooth loss function along the search direction. Dynamic MBSS updates the mini-batch at every function evaluation, resulting in a point-wise discontinuous loss function along the search direction. Line searches that adaptively resolve learning rates for static MBSS loss functions include the parabolic approximation line (PAL) search. Line searches that adaptively resolve learning rates for dynamic MBSS loss functions include probabilistic line searches, gradient-only line searches (GOLS) and quadratic approximations. (Wikipedia).

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