Dynamics of stochastic approximation algorithms (original) (raw)

Stochastic viability and invariance

Annali Scuola Normale di Pisa, 1990

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A deterministic analysis of stochastic approximation with randomized directions

1998

Abstract We study the convergence of two stochastic approximation algorithms with randomized directions: the simultaneous perturbation stochastic approximation algorithm and the random direction Kiefer-Wolfowitz algorithm. We establish deterministic necessary and sufficient conditions on the random directions and noise sequences for both algorithms, and these conditions demonstrate the effect of the “random” directions on the “sample-path” behavior of the algorithms studied.

ALGORITHMIC ANALYSIS OF STOCHASTIC MODELS The Changing Face of Mathematics

The progress in computing and communications technologies made in the last quarter of the past Century has not only ushered in the Information Age," but it has also in uenced the basic sciences, including mathematics, in fundamental ways. Thanks to the signi cantly increased computing power, mathematicians can now augment classical techniques of analysis, proof and solution with an algorithmic approach in a manner that enables the consideration of more complex models with wider applicability, and also obtain results with greater practical value to engineering. While providing powerful tools to the mathematician, the technologies, nevertheless, are also posing new challenges and problems, and opening many new vistas for further mathematical research.

Pruning and measures of uncertainty

Theoretical Informatics and Applications, 1978

L'accès aux archives de la revue « RAIRO. Informatique théorique » implique l'accord avec les conditions générales d'utilisation (http://www.numdam. org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/

Stochastic Approximation to Understand Simple Simulation Models

Journal of Statistical Physics, 2013

This paper illustrates how a deterministic approximation of a stochastic process can be usefully applied to analyse the dynamics of many simple simulation models. To demonstrate the type of results that can be obtained using this approximation, we present two illustrative examples which are meant to serve as methodological references for researchers exploring this area. Finally, we prove some convergence results for simulations of a family of evolutionary games, namely, intra-population imitation models in n-player games with arbitrary payoffs.

A.s. Approximation results for multiplicative stochastic integrals

Séminaire de Probabilités XVI 1980/81, 1982

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Exactness and Approximation of the Stochastic Simulation Algorithm

This short note intends to clarify about the applicability of the Stochastic Simulation Algorithm proposed by Gillespie for the analysis of systems of coupled biochemical reactions. The derivation of Gillespie's results is revisited to pinpoint those steps at which, depending on the validity of the assumptions adopted about the system to be studied, approximations may be introduced. We discuss about the ways the inaccuracies entailed by the approximations may propagate and affect simulation results.

Stochastic Approximation: From Statistical Origin to Big-Data, Multidisciplinary Applications

Statistical Science, 2021

Stochastic approximation was introduced in 1951 to provide a new theoretical framework for root finding and optimization of a regression function in the then-nascent field of statistics. This review shows how it has evolved in response to other developments in statistics, notably time series and sequential analysis, and to applications in artificial intelligence, economics, and engineering. Its resurgence in the Big Data Era has led to new advances in both theory and applications of this microcosm of statistics and data science.