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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.
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 ().
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 ...
Deep backward stochastic differential equation method is a numerical method that combines deep learning with Backward stochastic differential equation (BSDE). This method is particularly useful for solving high-dimensional problems in financial derivatives pricing and risk management .
Stochastic gradient descent; Backpropagation; ... As noted above, gradient descent tells us that our change for each weight should be proportional to the gradient.
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.
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
It also has StochasticGradient class for training a neural network using stochastic gradient descent, although the optim package provides much more options in this respect, like momentum and weight decay regularization.