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197
A Taxonomy of Global Optimization Methods Based on Response Surfaces
 Journal of Global Optimization
, 2001
"... Abstract. This paper presents a taxonomy of existing approaches for using response surfaces for global optimization. Each method is illustrated with a simple numerical example that brings out its advantages and disadvantages. The central theme is that methods that seem quite reasonable often have no ..."
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Cited by 121 (1 self)
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Abstract. This paper presents a taxonomy of existing approaches for using response surfaces for global optimization. Each method is illustrated with a simple numerical example that brings out its advantages and disadvantages. The central theme is that methods that seem quite reasonable often have nonobvious failure modes. Understanding these failure modes is essential for the development of practical algorithms that fulfill the intuitive promise of the response surface approach. Key words: global optimization, response surface, kriging, splines 1.
A Radial Basis Function Method for Global Optimization
 JOURNAL OF GLOBAL OPTIMIZATION
, 1999
"... We introduce a method that aims to find the global minimum of a continuous nonconvex function on a compact subset of R^d. It is assumed that function evaluations are expensive and that no additional information is available. Radial basis function interpolation is used to define a utility function. T ..."
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Cited by 49 (1 self)
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We introduce a method that aims to find the global minimum of a continuous nonconvex function on a compact subset of R^d. It is assumed that function evaluations are expensive and that no additional information is available. Radial basis function interpolation is used to define a utility function. The maximizer of this function is the next point where the objective function is evaluated. We show that, for most types of radial basis functions that are considered in this paper, convergence can be achieved without further assumptions on the objective function. Besides, it turns out that our method is closely related to a statistical global optimization method, the Palgorithm. A general framework for both methods is presented. Finally, a few numerical examples show that on the set of DixonSzego test functions our method yields favourable results in comparison to other global optimization methods.
Bayesian Treed Gaussian Process Models with an Application to Computer Modeling
 Journal of the American Statistical Association
, 2007
"... This paper explores nonparametric and semiparametric nonstationary modeling methodologies that couple stationary Gaussian processes and (limiting) linear models with treed partitioning. Partitioning is a simple but effective method for dealing with nonstationarity. Mixing between full Gaussian proce ..."
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Cited by 44 (15 self)
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This paper explores nonparametric and semiparametric nonstationary modeling methodologies that couple stationary Gaussian processes and (limiting) linear models with treed partitioning. Partitioning is a simple but effective method for dealing with nonstationarity. Mixing between full Gaussian processes and simple linear models can yield a more parsimonious spatial model while significantly reducing computational effort. The methodological developments and statistical computing details which make this approach efficient are described in detail. Illustrations of our model are given for both synthetic and real datasets. Key words: recursive partitioning, nonstationary spatial model, nonparametric regression, Bayesian model averaging 1
Gaussian Process Optimization in the Bandit Setting: No Regret and Experimental Design
"... Many applications require optimizing an unknown, noisy function that is expensive to evaluate. We formalize this task as a multiarmed bandit problem, where the payoff function is either sampled from a Gaussian process (GP) or has low RKHS norm. We resolve the important open problem of deriving regre ..."
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Cited by 44 (9 self)
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Many applications require optimizing an unknown, noisy function that is expensive to evaluate. We formalize this task as a multiarmed bandit problem, where the payoff function is either sampled from a Gaussian process (GP) or has low RKHS norm. We resolve the important open problem of deriving regret bounds for this setting, which imply novel convergence rates for GP optimization. We analyze GPUCB, an intuitive upperconfidence based algorithm, and bound its cumulative regret in terms of maximal information gain, establishing a novel connection between GP optimization and experimental design. Moreover, by bounding the latter in terms of operator spectra, we obtain explicit sublinear regret bounds for many commonly used covariance functions. In some important cases, our bounds have surprisingly weak dependence on the dimensionality. In our experiments on real sensor data, GPUCB compares favorably with other heuristical GP optimization approaches. 1.
Flexibility and Efficiency Enhancements for Constrained Global Design Optimization with Kriging Approximations
, 2002
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Simulated Annealing Algorithms For Continuous Global Optimization
, 2000
"... INTRODUCTION In this paper we consider Simulated Annealing algorithms (SA in what follows) applied to continuous global optimization problems, i.e. problems with the following form f = min x2X f(x); (1.1) where X ` ! n is a continuous domain, often assumed to be compact, which, combined with ..."
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Cited by 30 (1 self)
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INTRODUCTION In this paper we consider Simulated Annealing algorithms (SA in what follows) applied to continuous global optimization problems, i.e. problems with the following form f = min x2X f(x); (1.1) where X ` ! n is a continuous domain, often assumed to be compact, which, combined with the continuity or lower semicontinuity of f , guarantees the existence of the minimum value f . SA algorithms are based on an analogy with a physical phenomenon: while at high temperatures the molecules in a liquid move freely, if the temperature is slowly decreased the thermal mobility of the molecules is lost and they form a pure crystal which also corresponds to a state of minimum energy. If the temperature is decreased too quickly (the so called quenching) a liquid metal rather ends up in a polycrystalline or amorphous state with
A tutorial on Bayesian optimization of expensive cost functions, withapplicationtoactiveusermodeling andhierarchical reinforcement learning
, 2009
"... We present a tutorial on Bayesian optimization, a method of finding the maximum of expensive cost functions. Bayesian optimization employs the Bayesian technique of setting a prior over the objective function and combining it with evidence to get a posterior function. This permits a utilitybased se ..."
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Cited by 28 (2 self)
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We present a tutorial on Bayesian optimization, a method of finding the maximum of expensive cost functions. Bayesian optimization employs the Bayesian technique of setting a prior over the objective function and combining it with evidence to get a posterior function. This permits a utilitybased selection of the next observation to make on the objective function, which must take into account both exploration (sampling from areas of high uncertainty) and exploitation (sampling areas likely to offer improvement over the current best observation). We also present two detailed extensions of Bayesian optimization, with experiments—active user modelling with preferences, and hierarchical reinforcement learning— and a discussion of the pros and cons of Bayesian optimization based on our experiences. 1
Snobfit  Stable Noisy Optimization by Branch and Fit
"... this paper produces a userspeci ed number of suggested evaluation points in each step; proceeds by successive partitioning of the box (branch) and building local quadratic models ( t); combines local and global search and allows the user to determine which of both should be emphasized; h ..."
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Cited by 25 (5 self)
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this paper produces a userspeci ed number of suggested evaluation points in each step; proceeds by successive partitioning of the box (branch) and building local quadratic models ( t); combines local and global search and allows the user to determine which of both should be emphasized; handles local search from the best point with the aid of trust regions; allows for hidden constraints and assigns to such points a function value based on the function values of nearby feasible points
Active policy learning for robot planning and exploration under uncertainty
 IN PROCEEDINGS OF ROBOTICS: SCIENCE AND SYSTEMS
, 2007
"... This paper proposes a simulationbased active policy learning algorithm for finitehorizon, partiallyobserved sequential decision processes. The algorithm is tested in the domain of robot navigation and exploration under uncertainty. In such a setting, the expected cost, that must be minimized, is ..."
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Cited by 23 (1 self)
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This paper proposes a simulationbased active policy learning algorithm for finitehorizon, partiallyobserved sequential decision processes. The algorithm is tested in the domain of robot navigation and exploration under uncertainty. In such a setting, the expected cost, that must be minimized, is a function of the belief state (filtering distribution). This filtering distribution is in turn nonlinear and subject to discontinuities, which arise because constraints in the robot motion and control models. As a result, the expected cost is nondifferentiable and very expensive to simulate. The new algorithm overcomes the first difficulty and reduces the number of required simulations as follows. First, it assumes that we have carried out previous simulations which returned values of the expected cost for different corresponding policy parameters. Second, it fits a Gaussian process (GP) regression model to these values, so as to approximate the expected cost as a function of the policy parameters. Third, it uses the GP predicted mean and variance to construct a statistical measure that determines which policy parameters should be used in the next simulation. The process is then repeated using the new parameters and the newly gathered expected cost observation. Since the objective is to find the policy parameters that minimize the expected cost, this iterative active learning approach effectively tradesoff between exploration (in regions where the GP variance is large) and exploitation (where the GP mean is low). In our experiments, a robot uses the proposed algorithm to plan an optimal path for accomplishing a series of tasks, while maximizing the information about its pose and map estimates. These estimates are obtained with a standard filter for simultaneous localization and mapping. Upon gathering new observations, the robot updates the state estimates and is able to replan a new path in the spirit of openloop feedback control.
Exploration of Metamodeling Sampling Criteria for Constrained Global Optimization
 Engineering Optimization
, 2002
"... This paper focuses on a particular algorithm, Efficient Global Optimization (EGO) that uses kriging metamodels. Several infill sampling criteria are reviewed, namely criteria for selecting the points added to the data set for fitting the metamodel. The infill sampling criterion has a strong influenc ..."
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Cited by 21 (3 self)
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This paper focuses on a particular algorithm, Efficient Global Optimization (EGO) that uses kriging metamodels. Several infill sampling criteria are reviewed, namely criteria for selecting the points added to the data set for fitting the metamodel. The infill sampling criterion has a strong influence on how efficiently and accurately EGO locates the optimum. Variancereducing criteria substantially reduce the RMS error of the resulting metamodels, while other criteria influence how locally or globally EGO searches. Criteria that place more emphasis on global searching require more iterations to locate optima and do so less accurately than criteria emphasizing local search