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  2. Stochastic gradient descent - Wikipedia

    en.wikipedia.org/wiki/Stochastic_gradient_descent

    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.

  3. Backtracking line search - Wikipedia

    en.wikipedia.org/wiki/Backtracking_line_search

    In the stochastic setting, under the same assumption that the gradient is Lipschitz continuous and one uses a more restrictive version (requiring in addition that the sum of learning rates is infinite and the sum of squares of learning rates is finite) of diminishing learning rate scheme (see section "Stochastic gradient descent") and moreover ...

  4. Gradient descent - Wikipedia

    en.wikipedia.org/wiki/Gradient_descent

    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 ...

  5. Gradient method - Wikipedia

    en.wikipedia.org/wiki/Gradient_method

    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.

  6. Stochastic gradient Langevin dynamics - Wikipedia

    en.wikipedia.org/wiki/Stochastic_Gradient_Langev...

    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.

  7. Least mean squares filter - Wikipedia

    en.wikipedia.org/wiki/Least_mean_squares_filter

    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 ...

  8. Stochastic variance reduction - Wikipedia

    en.wikipedia.org/wiki/Stochastic_variance_reduction

    Stochastic variance reduced methods without acceleration are able to find a minima of within accuracy >, i.e. () in a number of steps of the order: ((+) ⁡ ()).The number of steps depends only logarithmically on the level of accuracy required, in contrast to the stochastic approximation framework, where the number of steps (/ ()) required grows proportionally to the accuracy required.

  9. Barzilai-Borwein method - Wikipedia

    en.wikipedia.org/wiki/Barzilai-Borwein_method

    The Barzilai-Borwein method [1] is an iterative gradient descent method for unconstrained optimization using either of two step sizes derived from the linear trend of the most recent two iterates. This method, and modifications, are globally convergent under mild conditions, [ 2 ] [ 3 ] and perform competitively with conjugate gradient methods ...