Abstract
This chapter addresses a few theoretical and practical issues raised by a class of stochastic optimization or approximation algorithms. These algorithms are efficient numerical tools in various applications and they are at the basis of the variance reduction techniques studied in the preceding chapter. We limit ourselves to a simple framework which allows us to get convergence results by means of dynamical systems and martingales theories without too many technical details. In this, we follow the very pedagogical approach in Benaïm and El Karoui (Chaînes de Markov et simulations; Martingales et stratégies, 2004).
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Graham, C., Talay, D. (2013). Stochastic Algorithms. In: Stochastic Simulation and Monte Carlo Methods. Stochastic Modelling and Applied Probability, vol 68. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39363-1_9
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DOI: https://doi.org/10.1007/978-3-642-39363-1_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39362-4
Online ISBN: 978-3-642-39363-1
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