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Simulated annealing (SA) is a probabilistic technique for approximating the global optimum of a given function. Specifically, it is a metaheuristic to approximate global optimization in a large search space for an optimization problem. For large numbers of local optima, SA can find the global optimum. [1]
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 ...
While it is sometimes possible to substitute gradient descent for a local search algorithm, gradient descent is not in the same family: although it is an iterative method for local optimization, it relies on an objective function’s gradient rather than an explicit exploration of the solution space.
By contrast, gradient descent methods can move in any direction that the ridge or alley may ascend or descend. Hence, gradient descent or the conjugate gradient method is generally preferred over hill climbing when the target function is differentiable. Hill climbers, however, have the advantage of not requiring the target function to be ...
Due to its resulting linear memory requirement, the L-BFGS method is particularly well suited for optimization problems with many variables. Instead of the inverse Hessian H k, L-BFGS maintains a history of the past m updates of the position x and gradient ∇f(x), where generally the history size m can be small (often <).
Such models are learned from the population by employing machine learning techniques and represented as probabilistic graphical models, from which new solutions can be sampled [112] [113] or generated from guided-crossover. [114] [115] Simulated annealing (SA)
Tabu search has several similarities with simulated annealing, as both involve possible downhill moves. In fact, simulated annealing could be viewed as a special form of TS, whereby we use "graduated tenure", that is, a move becomes tabu with a specified probability.
In the adaptive control literature, the learning rate is commonly referred to as gain. [2] In setting a learning rate, there is a trade-off between the rate of convergence and overshooting. While the descent direction is usually determined from the gradient of the loss function, the learning rate determines how big a step is taken in that ...