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Accelerated randomized stochastic optimization
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DOI：10.1214/aos/1059655913.png)
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摘要
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We propose a general class of randomized gradient estimates to be employed in a recursive search for the minimum of an unknown multivariate regression function. Here only two observations per iteration step are used. Special cases include random direction stochastic approximation (Kushner and Clark), simultaneous perturbation stochastic approximation (Spall) and a special kernel based stochastic approximation method (Polyak and Tsybakov). If the unknown regression is p-smooth (p greater than or equal to 2) at the point of minimum, these methods achieve the optimal rate of convergence O(n(-(p-1)/(2p))). For both the classical stochastic approximation scheme (Kiefer and Wolfowitz) and the averaging scheme (Ruppert and Polyak) the related asymptotic distributions are computed.
Keyword:
stochastic approximation
stochastic optimization
gradient estimation
randomization
asymptotic normality
optimal rates of convergence
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IF:
3.7
论文数:
2.8K
被引数:
2.9W
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