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Random Directions Stochastic Approximation with Deterministic Perturbations
, Bhatnagar S., , Fu M., Marcus S.I.
Published in IEEE
Volume: 65
Issue: 6
Pages: 2450 - 2465
We introduce deterministic perturbation (DP) schemes for the recently proposed random directions stochastic approximation, and propose new first-order and second-order algorithms. In the latter case, these are the first second-order algorithms to incorporate DPs. We show that the gradient and/or Hessian estimates in the resulting algorithms with DPs are asymptotically unbiased, so that the algorithms are provably convergent. Furthermore, we derive convergence rates to establish the superiority of the first-order and second-order algorithms, for the special case of a convex and quadratic optimization problem, respectively. Numerical experiments are used to validate the theoretical results. © 1963-2012 IEEE.
About the journal
JournalData powered by TypesetIEEE Transactions on Automatic Control
PublisherData powered by TypesetIEEE
Open AccessNo