Abstract
We studied SPSA-based gradient estimation techniques in the previous chapter. Along similar lines, we present in this chapter, smoothed functional (SF)-based estimators of the gradient. While SF is also based on simultaneously perturbing the parameter vector, unlike SPSA, for the purpose of perturbation, one uses a smoothing function that possesses certain properties. An alternate view of the SF approach is that the gradient is convolved with a smoothing function, which in turn could possibly help in finding the global minimum of the smoothed objective. We discuss SF-based algorithms where the smoothing is done using Gaussian and Cauchy density functions. The regular SF algorithms require only one measurement of the objective function. We also provide the two-measurement variants of all the algorithms presented.
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References
Bhatnagar, S.: Multiscale stochastic approximation algorithms with applications to ABR service in ATM networks. Ph.D. thesis, Department of Electrical Engineering. Indian Institute of Science, Bangalore, India (1997)
Bhatnagar, S.: Adaptive Newton-based smoothed functional algorithms for simulation optimization. ACM Transactions on Modeling and Computer Simulation 18(1), 2:1–2:35 (2007)
Bhatnagar, S., Borkar, V.S.: Multiscale chaotic SPSA and smoothed functional algorithms for simulation optimization. Simulation 79(10), 568–580 (2003)
Borkar, V.S.: Stochastic Approximation: A Dynamical Systems Viewpoint. Cambridge University Press and Hindustan Book Agency (Jointly Published), Cambridge and New Delhi (2008)
Chin, D.C.: Comparative study of stochastic algorithms for system optimization based on gradient approximation. IEEE Trans. Sys. Man. Cyber. Part B 27(2), 244–249 (1997)
Ghoshdastidar, D., Dukkipati, A., Bhatnagar, S.: q-Gaussian based smoothed functional algorithms for stochastic optimization. In: Proceedings of the IEEE International Symposium on Information Theory. IEEE Press, Boston (to appear, 2012)
Katkovnik, V.Y., Kulchitsky, Y.: Convergence of a class of random search algorithms. Automation Remote Control 8, 1321–1326 (1972)
Rubinstein, R.Y.: Simulation and the Monte Carlo Method. Wiley, New York (1981)
Styblinski, M.A., Tang, T.S.: Experiments in nonconvex optimization: stochastic approximation with function smoothing and simulated annealing. Neural Networks 3, 467–483 (1990)
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© 2013 Springer-Verlag London
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Bhatnagar, S., Prasad, H., Prashanth, L. (2013). Smoothed Functional Gradient Schemes. In: Stochastic Recursive Algorithms for Optimization. Lecture Notes in Control and Information Sciences, vol 434. Springer, London. https://doi.org/10.1007/978-1-4471-4285-0_6
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DOI: https://doi.org/10.1007/978-1-4471-4285-0_6
Publisher Name: Springer, London
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