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A conceptually simple extension of stochastic gradient descent makes the learning rate a decreasing function η t of the iteration number t, giving a learning rate schedule, so that the first iterations cause large changes in the parameters, while the later ones do only fine-tuning.
Gradient descent with momentum remembers the solution update at each iteration, and determines the next update as a linear combination of the gradient and the previous update. For unconstrained quadratic minimization, a theoretical convergence rate bound of the heavy ball method is asymptotically the same as that for the optimal conjugate ...
It allows for the efficient computation of gradients through random variables, enabling the optimization of parametric probability models using stochastic gradient descent, and the variance reduction of estimators. It was developed in the 1980s in operations research, under the name of "pathwise gradients", or "stochastic gradients".
In optimization, a gradient method is an algorithm to solve problems of the form min x ∈ R n f ( x ) {\displaystyle \min _{x\in \mathbb {R} ^{n}}\;f(x)} with the search directions defined by the gradient of the function at the current point.
Another way is the so-called adaptive standard GD or SGD, some representatives are Adam, Adadelta, RMSProp and so on, see the article on Stochastic gradient descent. In adaptive standard GD or SGD, learning rates are allowed to vary at each iterate step n, but in a different manner from Backtracking line search for gradient descent.
These include coordinate descent, [27] subgradient methods, least-angle regression (LARS), and proximal gradient methods. [28] Subgradient methods are the natural generalization of traditional methods such as gradient descent and stochastic gradient descent to the case in which the objective function is not differentiable at all points.
Neighbourhood components analysis is a supervised learning method for classifying multivariate data into distinct classes according to a given distance metric over the data. . Functionally, it serves the same purposes as the K-nearest neighbors algorithm and makes direct use of a related concept termed stochastic nearest neighbo
Natural gradient descent in the space of sample distributions [ edit ] Akimoto et al. [ 4 ] and Glasmachers et al. [ 5 ] discovered independently that the update of the distribution parameters resembles the descent in direction of a sampled natural gradient of the expected objective function value E f ( x ) {\displaystyle Ef(x)} (to be ...