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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".
SGLD can be applied to the optimization of non-convex objective functions, shown here to be a sum of Gaussians. Stochastic gradient Langevin dynamics (SGLD) is an optimization and sampling technique composed of characteristics from Stochastic gradient descent, a Robbins–Monro optimization algorithm, and Langevin dynamics, a mathematical extension of molecular dynamics models.
This technique is used in stochastic gradient descent and as an extension to the backpropagation algorithms used to train artificial neural networks. [29] [30] In the direction of updating, stochastic gradient descent adds a stochastic property. The weights can be used to calculate the derivatives.
Empirically, feature scaling can improve the convergence speed of stochastic gradient descent. In support vector machines, [2] it can reduce the time to find support vectors. Feature scaling is also often used in applications involving distances and similarities between data points, such as clustering and similarity search.
The algorithm starts with an initial estimate of the optimal value, , and proceeds iteratively to refine that estimate with a sequence of better estimates ,, ….The derivatives of the function := are used as a key driver of the algorithm to identify the direction of steepest descent, and also to form an estimate of the Hessian matrix (second derivative) of ().
Stochastic gradient descent (SGD) BFGS; Conjugate gradient; Regularization (L1 norm, L2 norm, & elastic net regularization) Flexible input - input features may be: Binary; Numerical; Categorical (via flexible feature-naming and the hash trick) Can deal with missing values/sparse-features; Other features
SPSA is a descent method capable of finding global minima, sharing this property with other methods such as simulated annealing. Its main feature is the gradient approximation that requires only two measurements of the objective function, regardless of the dimension of the optimization problem.