Application of Bayesian approach to numerical methods of global and stochastic optimization

By Jonas Mockus. 1994

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Taking the Human Out of the Loop: A Review of Bayesian Optimization (2016, methodology): “Meanwhile, in the former Soviet Union, Moˇckus and colleagues developed a multidimensional Bayesian optimization method using linear combinations of Wiener ﬁelds [115], [114].”
Freeze-Thaw Bayesian Optimization (2014, background): “A popular and effective acquisition function is the expected improvement (EI) criterion [15, 16], where φ and Φ , respectively, are the probability density function and cumulative distribution function of the standard normal distribution, x best is the input corresponding to the minimum output…”
A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning (2010, methodology): “This is a necessary condition for convergence under the assumptions of [Močkus, 1994].”
Multi-fidelity Bayesian Optimisation with Continuous Approximations (2017, methodology): “While there are several techniques for BO (de Fre-itas et al., 2012; Hern´andez-Lobato et al., 2014; Jones et al., 1998; Mockus, 1994; Thompson, 1933), our work will build on the Gaussian process upper conﬁdence bound ( GP-UCB ) algorithm of Srinivas et al. (2010).”
Flexibility and efficiency enhancements for constrained global design optimization with kriging approximations. (2002, background): “Both Mockus and Žilinskas also successfully extended Bayesian techniques to n dimensions [58],[59], [103], [106].”
Learning a strategy for adapting a program analysis via bayesian optimisation (2015, background): “Bayesian optimisation [3, 15] is a generic algorithm for solving an optimisation where an objective function does not have a nice mathematical structure such as gradient and convexity, and evaluating this function is expensive.”
Convergence Rates of Efficient Global Optimization Algorithms (2011, methodology): “ strategy is expected improvement. It is sometimes called Bayesian optimization, and ﬁrst appeared in the work of Mockus as a Bayesian decision-theoretic solution to the problem (Mockus et al., 1978; Mockus, 1994). Contemporary computers were not powerful enough to implement the technique in full, a”
Multi-fidelity Gaussian Process Bandit Optimisation (2016, methodology): “While there are several techniques for BO (Hernández-Lobato et al., 2014; Jones et al., 1998; Mockus, 1994; Thompson, 1933), of particular interest to us is the Gaussian process upper confidence bound (GP-UCB) algorithm of Srinivas et al. (2010).”
High Dimensional Bayesian Optimisation and Bandits via Additive Models (2015, unknown): “GP-UCB on D th order kernel”
Gaussian Processes for history-matching: application to an unconventional gas reservoir (2017, background): “More specifically, Mockus [41] showed that the use of Gaussian distribution is well suited for optimization tasks and can provide satisfactory results.”
The Knowledge-Gradient Policy for Correlated Normal Beliefs (2009, methodology): “Stuckman (1988) as well as Mockus (1989, 1994) ) extended these two methods to multiple”
Complete search in continuous global optimization and constraint satisfaction (2004, methodology): “…1990, Kostrowicki and Scheraga 1996, Moré and Wu 1997, Stillinger 1985); response surface techniques, including Bayesian stochastic techniques Mockus (1989, 1994) and related techniques (Björkman and Holmström 2000, Jones 2001, Jones, Schonlau and Welch 1998); nonmonotonic search…”
Maximizing acquisition functions for Bayesian optimization (2018, background): “From a high-level perspective, BO can be understood as the application of Bayesian decision theory to optimization problems [11, 14, 45].”