Stochastic approximation and its applications

By Han-Fu Chen. 2002

439 citations recorded by the source corpus.

Subfields: Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/bcea4ae4e54820ce7c41bb45f8a90fc5bd98fd53

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In Control and Systems Engineering

Citations in the corpus

Distributed Seeking of Nash Equilibria With Applications to Mobile Sensor Networks (2012, background): “5) are stronger than in [40], but they are sufficient for our convergence analysis.”
Decentralized Parameter Estimation by Consensus Based Stochastic Approximation (2007, background): “1 of the parameter estimates under mild conditions in more complex tasks of multivariable dynamic system identification [60], [61], [62].”
A Concentration Bound for Stochastic Approximation via Alekseev’s Formula (2015, methodology): “oise eﬀects average out so that the asymptotic behavior of a SA method is determined by that of a suitable deterministic ODE, often referred to as the limiting ODE. For more details on the above, see [7, 6, 12, 15, 26, 5]. ∗Supported partially by an IBM PhD fellowship. †Supported in part by a J. C. ”
Central Limit Theorems for Stochastic Approximation with controlled Markov chain dynamics (2013, methodology): “Fabian [14], Kushner and Huang [21], Bouton [7], Buche and Kushner [8], Chen [9] Chap.”
Stochastic Consensus Seeking With Noisy and Directed Inter-Agent Communication: Fixed and Randomly Varying Topologies (2010, background): “…stochastic systems for the purpose of either function optimization, root-finding, or system identification, it has long been known that a properly decreasing gain for the correction term is essential for obtaining convergence, and there exists a vast literature on these broad areas [3], [6], [8].”
Language modeling with neural trans-dimensional random fields (2017, background): “The convergence of SA has been studied under various conditions [23,24,25].”
Stochastic Equilibrium Problems and Stochastic Mathematical Programs with Equilibrium Constraints: A Survey 1 (2009, background): “applied to solving various stochastic problems; see for instance [8, 23, 49] and the references therein.”
Learning Trans-Dimensional Random Fields with Applications to Language Modeling (2018, methodology): “The convergence of SA has been studied under various regularity conditions [17], [18].”
Trans-dimensional Random Fields for Language Modeling (2015, methodology): “We develop a stochastic approximation algorith-m using Markov chain Monte Carlo to estimate the parameters λ and the normalization constants Z 1 ( λ ) , ..., Z m ( λ ) (Benveniste et al., 1990; Chen, 2002).”
A Resampling-Based Stochastic Approximation Method for Analysis of Large Geostatistical Data (2013, methodology): “The convergence of the modified algorithm can be shown for a wide class of mean field functions, see, for example, Chen (2002).”
Coordination and Consensus of Networked Agents with Noisy Measurements: Stochastic Algorithms and Asymptotic Behavior (2009, background): “Notice that (A2′)(ii) is a typical condition used in classical stochastic approximation theory [11, 24].”
Models for longitudinal network datain (2005, methodology): “The idea of regarding the dynamics of social phenomena as being the result of a continuous-time process, even though observations are made at discrete time points, was proposed already by Coleman (1964). Several methods have been proposed for analyzing repeated observations on social networks using ”
On‐line expectation–maximization algorithm for latent data models (2007, methodology): “In general settings, the stability of the algorithm can be enforced by truncating the algorithm updates, either on a ﬁxed set (see, e.g., Kushner and Yin, 2003, chapter 2) or on an expanding sequence of sets (see, e.g., Chen, 2002, chapter 2, or Andrieu et al., 2005).”