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Stochastic gradient descent competes with the L-BFGS algorithm, [citation needed] which is also widely used. Stochastic gradient descent has been used since at least 1960 for training linear regression models, originally under the name ADALINE. [25] Another stochastic gradient descent algorithm is the least mean squares (LMS) adaptive filter.
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".
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 ...
Stochastic gradient descent; Backpropagation; ... As noted above, gradient descent tells us that our change for each weight should be proportional to the gradient.
For the case of a function with at most countably many critical points (such as a Morse function) and compact sublevels, as well as with Lipschitz continuous gradient where one uses standard GD with learning rate <1/L (see the section "Stochastic gradient descent"), then convergence is guaranteed, see for example Chapter 12 in Lange (2013 ...
If is chosen to be large, the amount with which the weights change depends heavily on the gradient estimate, and so the weights may change by a large value so that gradient which was negative at the first instant may now become positive. And at the second instant, the weight may change in the opposite direction by a large amount because of the ...
Strictly speaking, the term backpropagation refers only to an algorithm for efficiently computing the gradient, not how the gradient is used; but the term is often used loosely to refer to the entire learning algorithm – including how the gradient is used, such as by stochastic gradient descent, or as an intermediate step in a more ...
The deep BSDE method constructs neural networks to approximate the solutions for and , and utilizes stochastic gradient descent and other optimization algorithms for training. [1] The fig illustrates the network architecture for the deep BSDE method.