Introduction to Stochastic Search and Optimization: Estimation, Simulation, and Control

By Tim Hesterberg. 2004

1,336 citations recorded by the source corpus.

Subfields: Optimization & Training, Probabilistic & Bayesian Methods

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Citations in the corpus

Variational Inference: A Review for Statisticians (2016, background): “This idea has blossomed (Kushner and Yin 1997; Spall 2003).”
Stochastic First- and Zeroth-Order Methods for Nonconvex Stochastic Programming (2013, methodology): “However, it is usually diﬃcult to implement the “asymptotically optimal” stepsize policy, especially in the beginning, so that the algorithms often perform poorly in practice (e.g., [39, Section 4.5.3]).”
Empirically Evaluating Multiagent Learning Algorithms (2014, methodology): “We also tested the Global Stochastic Approximation algorithm, GSA , of Spall (2003); see Table VII.”
Accelerated gradient methods for nonconvex nonlinear and stochastic programming (2013, background): “, [10,11,15,23,30,31,33]) require the convexity assumption about Ψ .”
GA: A Package for Genetic Algorithms in R (2013, background): “…which are able to solve optimization problems of the type described in Equation 1, both for continuous (whether di ↵ erentiable or not) and discrete functions (A ↵ enzeller and Winkler 2009; Back, Fogel, and Michalewicz 2000a,b; Coley 1999; Eiben and Smith 2003; Haupt and Haupt 2004; Spall 2003).”
Quality and Diversity Optimization: A Unifying Modular Framework (2017, background): “species that are well adapted to their environment, Evolutionary Computation has a long history in the domain of optimization, particularly in stochastic optimization [6].”
Adaptive stepsizes for recursive estimation with applications in approximate dynamic programming (2006, background): “It can be shown that in certain cases a biased estimator can give a lower variance than the sample mean (Spall, 2003), p. [334], however we limit ourselves to estimators that are unbiased.”
Machine Learning in Materials Science (2016, neutral): “( ) ( ) ( ) ( ) | , , | , P f g P f g P f g P = D D D [20]”
Optimal Rates for Zero-Order Convex Optimization: The Power of Two Function Evaluations (2013, background): “Similarly, the field of simulation-based optimization provides many examples of problems in which optimization is performed based only on function values [1], [5], [9].”
Theoretical connections between optimization algorithms based on an approximate gradient (2013, methodology): “(14) Following the guidelines of Spall [33, 36] for SPSA, the step size αk and perturbation size ck , respectively, are defined by the following equations: αk = a (k + A + 1)β (15) and ck = c (k + 1)γ , (16) where a, A, c, β, and γ are positive real numbers which satisfy A ≥ 0, β − 2γ > 0 and 3γ − (”
A Survey of Optimization Methods From a Machine Learning Perspective (2019, methodology): “This reminds us of an attractive technique to handle large data sets: stochastic optimization [97], [192], [194].”
Policy Gradient Methods for Robotics (2006, neutral): “There are different ways of choosing the reference value J ref , e.g. forward-difference estimators with J ref = J ( θ h ) and central-difference estimators with J ref = J ( θ h − ∆ θ i ) .”
Grasshopper Optimisation Algorithm: Theory and application (2017, background): “8) and the distances between grasshoppers are normalised in [1,4] in each iteration.”
Joint Training of Generic CNN-CRF Models with Stochastic Optimization (2015, background): “We refer to [25,26] for details, for the cases of both convex and non-convex functions f ( θ ).”
Big Data Creates New Opportunities for Materials Research: A Review on Methods and Applications of Machine Learning for Materials Design (2019, positive): “Either deterministic [57] or stochastic algorithms [58] can be employed to solve the formulated optimization problem for which the optimal materials are identified.”
Stochastic variational inference (2012, methodology): “As we mentioned above, the main idea in this work is to use stochastic optimization (Robbins and Monro, 1951; Spall, 2003).”
Regression Density Estimation With Variational Methods and Stochastic Approximation (2012, methodology): “Under regularity conditions (Spall 2003), the λ(k) will converge to a local maximum of the lower bound.”