Analysis of Recursive Stochastic Algorithms

By Tamer Basar. 2001

576 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/b59515a2139ba9d19a68c5c7b969c3adafbb6625

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In Artificial Intelligence

Citations in the corpus

Stochastic Approximations and Differential Inclusions (2005, background): “The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.”
Locally Stationary Processes (2011, background): “…investigated over the last 30 years in different scientific communities: by system theorists under the name “recursive identification methods” (cf. Ljung (1977); Ljung and Söderström (1983)), in the stochastic approximation community (cf. Benveniste, Métivier and Priouret (1990); Kushner and…”
Stochastic Variance Reduction for Nonconvex Optimization (2016, background): “Sgd dates at least to the seminal work (Robbins & Monro, 1951); and since then it has been developed in several directions (Poljak & Tsypkin, 1973; Ljung, 1977; Bottou, 1991; Kushner & Clark, 2012).”
Empirical Dynamic Programming (2013, methodology): “method [28, 12], establishing rate of convergence has been quite difficult [22].”
Two-Timescale Networks for Nonlinear Value Function Approximation (2019, methodology): “To analyze the long-run behaviour of our algorithm, we employ the ODE based analysis (Borkar, 2008; Kushner and Yin, 2003; Ljung, 1977) of the stochastic recursive algorithms.”
Stochastic Gradient Descent on Riemannian Manifolds (2011, background): “It has had a long history in optimization and control with numerous applications (e.g. [19, 6, 36]).”
Control: A perspective (2014, background): “Similar issues had arisen in analysis of recursive algorithms such as stochastic approximation and recursive identification of ARMAX systems; the prior work paved the way for the analysis of the stochastic adaptive control systems [436,613,407,409,140,406].”
Streaming PCA and Subspace Tracking: The Missing Data Case (2018, background): “We can see that the theoretical prediction given by the ODEs (40) and (41) can accurately characterize the actual dynamic performance of the three algorithms.”
Adaptive Expectations, Underpa-rameterization and the Lucas Critique (2006, unknown): “For γt = 1/t we obtain βt = βt−1 + t −1(πt − βt−1), (8)”
Analysis of nonsmooth stochastic approximation: the differential inclusion approach (2018, methodology): “A powerful method to analyze stochastic gradient algorithm, introduced in the early works by [28] and [26] is the ordinary differential equation (ODE) method.”
A cautionary perspective on cross-layer design (2005, background): “The slower system can be regarded as seeing the averaged value of the parameter, and its stability implies the stability of the overall system under some conditions [9].”
Aligning Popularity and Quality in Online Cultural Markets (2021, methodology): “The ODE method (Ljung 1977) relates the recurrence Equation 5 with the ordinary differential equation ẋ = F (x).”