Bayesian Algorithms for One-Dimensional Global Optimization

By M. Locatelli. 1997

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Citations in the corpus

An evaluation of adaptive surrogate modeling based optimization with two benchmark problems (2014, methodology): “Some previous findings have suggested that the MEI method is capable to finding the global minimum asymptotically (Locatelli, 1997).”
Taking the Human Out of the Loop: A Review of Bayesian Optimization (2016, background): “[102] M.”
A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning (2010, methodology): “There exist several consistency proofs for this algorithm in the one-dimensional setting [Locatelli, 1997] and one for a simplification of the algorithm using simplicial partitioning in higher dimensions [Žilinskas and Žilinskas, 2002].”
Portfolio Allocation for Bayesian Optimization (2010, methodology): “Consistency of the method was shown in [27] for 1D processes and in [39] for general Gaussian processes with an acquisition function known as expected improvement.”
Multi-fidelity optimization via surrogate modelling (2007, background): “…using deterministic computer experiments, and guarantees global convergence; given that there is no possibility of re-sampling, as the number of updates based on the maximum E [I(x)] increases, the design space will become densely populated and so the global optimum will be found (Locatelli 1997).”
Geometric Filtration Using Proper Orthogonal Decomposition for Aerodynamic Design Optimization (2010, background): “Perhaps given enough time and updates, and using a better updating strategy such as expected improvement, one would expect the traditional kriging strategy to approach the global optimum [37,38] that the GA is assumed to have obtained.”
Convergence Rates of Efficient Global Optimization Algorithms (2011, background): “ocess ensures the choice of observations is invariant under translation and scaling of f, and is believed to be more eﬃcient (Jones et al., 1998, §2). It has a profound eﬀect on convergence, however: Locatelli (1997, §3.2) shows that, for a Brownian motion prior with estimated parameters, expected i”
A Bayesian exploration-exploitation approach for optimal online sensing and planning with a visually guided mobile robot (2009, background): “The objective of Bayesian optimization is to find the minimum of the cost function with as few cost evaluations as possible (Kushner 1964; Jones et al. 1998; Locatelli 1997; Mockus et al. 1978).”
Efficient Global Optimization of Expensive Black-Box Functions (1998, background): “Although we have not proved this conjecture, interested readers might consult the work of Marco Locatelli [20] who has proved a similar theorem for a related one-dimensional Bayesian algorithm.”
Global optimization based on a statistical model and simplicial partitioning (2002, methodology): “Extensive testing has shown that the implemented algorithms favorably compete with algorithms based on other approaches [7,8].”
Flexibility and efficiency enhancements for constrained global design optimization with kriging approximations. (2002, methodology): “Locatelli allowed for the Wiener model parameter σ to be fit iteratively during the optimization, enabling a more accurate model of the variance [53].”
Convergence properties of the expected improvement algorithm with fixed mean and covariance functions (2007, unknown): “In the case of the EI algorithm, this property was proved by Locatelli (1997), with d = 1, X = [0 , 1] and ξ a Brownian motion.”