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In mathematical optimization, a trust region is the subset of the region of the objective function that is approximated using a model function (often a quadratic).If an adequate model of the objective function is found within the trust region, then the region is expanded; conversely, if the approximation is poor, then the region is contracted.
LMA can also be viewed as Gauss–Newton using a trust region approach. The algorithm was first published in 1944 by Kenneth Levenberg , [ 1 ] while working at the Frankford Army Arsenal . It was rediscovered in 1963 by Donald Marquardt , [ 2 ] who worked as a statistician at DuPont , and independently by Girard, [ 3 ] Wynne [ 4 ] and Morrison.
Powell's dog leg method, also called Powell's hybrid method, is an iterative optimisation algorithm for the solution of non-linear least squares problems, introduced in 1970 by Michael J. D. Powell. [1] Similarly to the Levenberg–Marquardt algorithm, it combines the Gauss–Newton algorithm with gradient descent, but it uses an explicit trust ...
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It addressed the instability issue of another algorithm, the Deep Q-Network (DQN), by using the trust region method to limit the KL divergence between the old and new policies. However, TRPO uses the Hessian matrix (a matrix of second derivatives) to enforce the trust region, but the Hessian is inefficient for large-scale problems. [1]
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Since the update can be indefinite, the L-SR1 algorithm is suitable for a trust-region strategy. Because of the limited-memory matrix, the trust-region L-SR1 algorithm scales linearly with the problem size, just like L-BFGS.
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