2015/02/19 by Prashanth L. A., L. A. Prashanth, Shalabh Bhatnagar +7
Computer Science · Decision Sciences · Engineering · Mathematics · #Advanced Adaptive Filtering Techniques #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Neural Networks and Applications #Optimization and Control (math.OC) #Simulation Techniques and Applications #cs.LG #math.OC
paper · pdf · doi:10.48550/arxiv.1502.05577
openalex publication_date 2015/02/19 · arxiv created 2015/08/08 · arxiv updated 2015/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present novel algorithms for simulation optimization using random directions stochastic approximation (RDSA). These include first-order (gradient) as well as second-order (Newton) schemes. We incorporate both continuous-valued as well as discrete-valued perturbations into both our algorithms. The former are chosen to be independent and identically distributed (i.i.d.) symmetric, uniformly distributed random variables (r.v.), while the latter are i.i.d., asymmetric, Bernoulli r.v.s. Our Newton algorithm, with a novel Hessian estimation scheme, requires N-dimensional perturbations and three loss measurements per iteration, whereas the simultaneous perturbation Newton search algorithm of [1] requires 2N-dimensional perturbations and four loss measurements per iteration. We prove the unbiasedness of both gradient and Hessian estimates and asymptotic (strong) convergence for both first-order and second-order schemes. We also provide asymptotic normality results, which in particular establish that the asymmetric Bernoulli variant of Newton RDSA method is better than 2SPSA of [1]. Numerical experiments are used to validate the theoretical results.