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482
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 235 (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 non-obvious 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.
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 125 (13 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 GP-UCB, an intuitive upper-confidence 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, GP-UCB compares favorably with other heuristical GP optimization approaches. 1.
Sequential Model-Based Optimization for General Algorithm Configuration (extended version)
"... Abstract. State-of-the-art algorithms for hard computational problems often expose many parameters that can be modified to improve empirical performance. However, manually exploring the resulting combinatorial space of parameter settings is tedious and tends to lead to unsatisfactory outcomes. Recen ..."
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Cited by 107 (27 self)
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Abstract. State-of-the-art algorithms for hard computational problems often expose many parameters that can be modified to improve empirical performance. However, manually exploring the resulting combinatorial space of parameter settings is tedious and tends to lead to unsatisfactory outcomes. Recently, automated approaches for solving this algorithm configuration problem have led to substantial improvements in the state of the art for solving various problems. One promising approach constructs explicit regression models to describe the dependence of target algorithm performance on parameter settings; however, this approach has so far been limited to the optimization of few numerical algorithm parameters on single instances. In this paper, we extend this paradigm for the first time to general algorithm configuration problems, allowing many categorical parameters and optimization for sets of instances. We experimentally validate our new algorithm configuration procedure by optimizing a local search and a tree search solver for the propositional satisfiability problem (SAT), as well as the commercial mixed integer programming (MIP) solver CPLEX. In these experiments, our procedure yielded state-of-the-art performance, and in many cases outperformed the previous best configuration approach. 1
Complete search in continuous global optimization and constraint satisfaction
- ACTA NUMERICA 13
, 2004
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Use of Kriging Models to Approximate Deterministic Computer Models
- AIAA Journal
, 2005
"... 1 Address all correspondences to this author. Phone/fax: (814) 865-5930/863-4128. The use of kriging models for approximation and global optimization has been steadily on the rise in the past decade. The standard approach used in the Design and Analysis of Computer Experiments (DACE) is to use an Or ..."
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Cited by 92 (2 self)
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1 Address all correspondences to this author. Phone/fax: (814) 865-5930/863-4128. The use of kriging models for approximation and global optimization has been steadily on the rise in the past decade. The standard approach used in the Design and Analysis of Computer Experiments (DACE) is to use an Ordinary kriging model to approximate a deterministic computer model. Universal and Detrended kriging are two alternative types of kriging models. In this paper, a description on the basics of kriging is given, highlighting the similarities and differences between these three different types of kriging models and the underlying assumptions behind each. A comparative study on the use of three different types of kriging models is then presented using six test problems. The methods of Maximum Likelihood Estimation (MLE) and Cross-Validation (CV) for model parameter estimation are compared for the three kriging model types. A one-dimension problem is first used to visualize the differences between the different models. In order to show applications in higher dimensions, four two-dimension and a 5-dimension problem are also given.
A tutorial on Bayesian optimization of expensive cost functions, with application to active user modeling and hierarchical reinforcement learning
, 2010
"... 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 utility-based se ..."
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Cited by 91 (11 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 utility-based 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.
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 77 (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 P-algorithm. A general framework for both methods is presented. Finally, a few numerical examples show that on the set of Dixon-Szego test functions our method yields favourable results in comparison to other global optimization methods.
Flexibility and Efficiency Enhancements for Constrained Global Design Optimization with Kriging Approximations
, 2002
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Adaptive submodularity: Theory and applications in active learning and stochastic optimization
- J. Artificial Intelligence Research
, 2011
"... Many problems in artificial intelligence require adaptively making a sequence of decisions with uncertain outcomes under partial observability. Solving such stochastic optimization problems is a fundamental but notoriously difficult challenge. In this paper, we introduce the concept of adaptive subm ..."
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Cited by 70 (15 self)
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Many problems in artificial intelligence require adaptively making a sequence of decisions with uncertain outcomes under partial observability. Solving such stochastic optimization problems is a fundamental but notoriously difficult challenge. In this paper, we introduce the concept of adaptive submodularity, generalizing submodular set functions to adaptive policies. We prove that if a problem satisfies this property, a simple adaptive greedy algorithm is guaranteed to be competitive with the optimal policy. In addition to providing performance guarantees for both stochastic maximization and coverage, adaptive submodularity can be exploited to drastically speed up the greedy algorithm by using lazy evaluations. We illustrate the usefulness of the concept by giving several examples of adaptive submodular objectives arising in diverse AI applications including management of sensing resources, viral marketing and active learning. Proving adaptive submodularity for these problems allows us to recover existing results in these applications as special cases, improve approximation guarantees and handle natural generalizations. 1.
An informational approach to the global optimization of expensive-to-evaluate functions
, 2008
"... In many global optimization problems motivated by engineering applications, the number of function evaluations is severely limited by time or cost. To ensure that each of these evaluations contributes to the localization of good candidates for the role of global minimizer, a sequential choice of eva ..."
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Cited by 48 (6 self)
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In many global optimization problems motivated by engineering applications, the number of function evaluations is severely limited by time or cost. To ensure that each of these evaluations contributes to the localization of good candidates for the role of global minimizer, a sequential choice of evaluation points is usually carried out. In particular, when Kriging is used to interpolate past evaluations, the uncertainty associated with the lack of information on the function can be expressed and used to compute a number of criteria accounting for the interest of an additional evaluation at any given point. This paper introduces minimizer entropy as a new Kriging-based criterion for the sequential choice of points at which the function should be evaluated. Based on stepwise uncertainty reduction, it accounts for the informational gain on the minimizer expected from a new evaluation. The criterion is approximated using conditional simulations of the Gaussian process model behind Kriging, and then inserted into an algorithm similar to the Efficient Global Optimization (EGO) algorithm. An empirical comparison is carried out between our criterion and expected improvement, a standard criterion in the literature. Experimental results indicate major evaluation savings over EGO. Finally, the method is extended to robust optimization problems, where both the factors to be tuned and the function evaluations are corrupted by noise.
