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- W1522894549 abstract "We present the first adaptive random directions Newton algorithm under i.i.d., symmetric, uniformly distributed perturbations for a general problem of optimization under noisy observations. We also present a simple gradient search scheme under the aforementioned perturbation random variates. Our Newton algorithm requires generating $N$ perturbation variates and three simulations at each iteration unlike the well studied simultaneous perturbation Newton search algorithm of Spall (2000) that requires 2N iterates and four simulations. We prove the convergence of our algorithms to a local minimum and also present rate of convergence results. Our asymptotic mean square errors (AMSE) analysis indicates that our gradient algorithm requires 60% less number of simulations to achieve a given accuracy as compared to a similar algorithm in 60% less number of simulations to Kushner and Clark (1978); Chin (1997) that incorporates Gaussian perturbations. Moreover, our adaptive Newton search algorithm results in an AMSE that is on par and sometimes even better than the Newton algorithm of Spall (2000). Our experiments are seen to validate the theoretical observations. In particular, our experiments show that our Newton algorithm 2RDSA requires only 75% of the total number of loss function measurements as required by the Newton algorithm of Spall (2000) while providing the same accuracy levels as the latter." @default.
- W1522894549 created "2016-06-24" @default.
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- W1522894549 date "2015-02-19" @default.
- W1522894549 modified "2023-09-27" @default.
- W1522894549 title "Adaptive system optimization using (simultaneous) random directions stochastic approximation." @default.
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