A New Method of Locating the Maximum Point of an Arbitrary Multipeak Curve in the Presence of Noise

By Harold J. Kushner. 1964

Subfields: Mathematical Optimization, Numerical Methods & Scientific Computing

How researchers see this paper

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

In Mathematical Optimization

In Numerical Methods & Scientific Computing

Citations in the corpus

Scalable Bayesian Optimization Using Deep Neural Networks (2015, background): “Note that numerous alternate acquisition functions and combinations thereof have been proposed (Kushner, 1964; Srinivas et al., 2010; Hoﬀ-man et al., 2011), which could be used without aﬀect-ing the analytic properties of our approach.”
Hyper-Parameter Optimization: A Review of Algorithms and Applications (2020, background): “3), but Gaussian process (GP) (Rasmussen, 2003) is overwhelmingly the most widely used. Various acquisition functions have been proposed in previous studies, including the probability of improvement (Kushner, 1964), GP upper condence bound (GP-UCB) (Lai and Robbins, 1985; Srinivas et al., 2009), pre”
BANANAS: Bayesian Optimization with Neural Architectures for Neural Architecture Search (2019, methodology): “2009), expected improvement (EI) (Močkus 1975), and probability of improvement (PI) (Kushner 1964).”
Automated Machine Learning: State-of-The-Art and Open Challenges (2019, background): “Bayesian Optimization is one of the state-of-the-art blackbox optimization techniques which is tailored for expensive objective functions [69, 134, 88, 55].”
Taking the Human Out of the Loop: A Review of Bayesian Optimization (2016, methodology): “In the nonparametric setting, Kushner [91] used Wiener processes for unconstrained 1-D optimization problems.”
Learning to Learn for Global Optimization of Black Box Functions (2016, background): “…Hennig and Schuler, 2012, Russo and Van Roy, 2014, Shahriari et al., 2014, Hern ´ andez-Lobato et al., 2015], probability of improvement [Kushner, 1964, Jones et al., 1998], expected improvement [Moˇckus et al., 1978, Jones et al., 1998, Jones, 2001, Brochu et al., 2009, Snoek et al., 2012, Wang…”
Input Warping for Bayesian Optimization of Non-Stationary Functions (2014, background): “Numerous acquisition functions and combinations thereof have been proposed [e.g., Kushner, 1964, Srinivas et al., 2010, Hoffman et al., 2011].”
Inductive Transfer for Neural Architecture Optimization (2019, methodology): “Else, the probability of improvement (Kushner, 1964) is computed (Line 5).”
An Experimental Evaluation of Bayesian Optimization on Bipedal Locomotion (2014, methodology): “Bayesian Optimization Bayesian optimization is an iterative model-based global optimization method [7, 5, 11, 1].”
Surrogate-based methods for black-box optimization (2017, background): “This is called the Probability of improvement (PI) at x and is formally deﬁned as follows [34,39,58] 2 : here Φ is the normal cumulative distribution function.”