Bi-objective Decisions and Partition-Based Methods in Bayesian Global Optimization

[1]  James M. Calvin Probability Models in Global Optimization , 2016, Informatica.

[2]  A. Zilinskas,et al.  On the Convergence of the P-Algorithm for One-Dimensional Global Optimization of Smooth Functions , 1999 .

[3]  Warren B. Powell,et al.  The Knowledge-Gradient Policy for Correlated Normal Beliefs , 2009, INFORMS J. Comput..

[4]  Eric Walter,et al.  An informational approach to the global optimization of expensive-to-evaluate functions , 2006, J. Glob. Optim..

[5]  Andreas Krause,et al.  Efficient High Dimensional Bayesian Optimization with Additivity and Quadrature Fourier Features , 2018, NeurIPS.

[6]  Balázs Kégl,et al.  Surrogating the surrogate: accelerating Gaussian-process-based global optimization with a mixture cross-entropy algorithm , 2010, ICML.

[7]  Nando de Freitas,et al.  A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning , 2010, ArXiv.

[8]  Nando de Freitas,et al.  Bayesian Optimization in a Billion Dimensions via Random Embeddings , 2013, J. Artif. Intell. Res..

[9]  Andreas Krause,et al.  Information-Theoretic Regret Bounds for Gaussian Process Optimization in the Bandit Setting , 2009, IEEE Transactions on Information Theory.

[10]  Jonathan W. Pillow,et al.  Exploiting gradients and Hessians in Bayesian optimization and Bayesian quadrature. , 2017, 1704.00060.

[11]  Matt J. Kusner,et al.  Bayesian Optimization with Inequality Constraints , 2014, ICML.

[12]  Alan Fern,et al.  Bayesian Optimization with Resource Constraints and Production , 2016, ICAPS.

[13]  Alán Aspuru-Guzik,et al.  Parallel and Distributed Thompson Sampling for Large-scale Accelerated Exploration of Chemical Space , 2017, ICML.

[14]  Guilherme Ottoni,et al.  Constrained Bayesian Optimization with Noisy Experiments , 2017, Bayesian Analysis.

[15]  Roman Garnett,et al.  Automating Bayesian optimization with Bayesian optimization , 2018, NeurIPS.

[16]  Algirdas Makauskas On a possibility to use gradients in statistical models of global optimization of objective functions , 1991 .

[17]  James M. Calvin,et al.  A lower bound on complexity of optimization on the Wiener space , 2007, Theor. Comput. Sci..

[18]  Donald R. Jones,et al.  Global versus local search in constrained optimization of computer models , 1998 .

[19]  Zengyi Dou,et al.  Bayesian global optimization approach to the oil well placement problem with quantified uncertainties , 2015 .

[20]  Julius Zilinskas,et al.  Globally-biased Disimpl algorithm for expensive global optimization , 2014, Journal of Global Optimization.

[21]  Stephen J. Roberts,et al.  A Bayesian optimization approach to compute the Nash equilibria of potential games using bandit feedback , 2018, Comput. J..

[22]  James M. Calvin,et al.  Bi-objective decision making in global optimization based on statistical models , 2019, J. Glob. Optim..

[23]  Peter I. Frazier,et al.  Parallel Bayesian Global Optimization of Expensive Functions , 2016, Oper. Res..

[24]  Antanas Žilinskas Algorithm. 44. MIMUN. Optimization of one-dimensional multimodal functions in the presence of noise , 1980 .

[25]  Harrison Prosper,et al.  Deep Learning and Bayesian Methods , 2017 .

[26]  A. Zilinskas,et al.  Including the derivative information into statistical models used in global optimization , 2019 .

[27]  Nando de Freitas,et al.  Bayesian Optimization in High Dimensions via Random Embeddings , 2013, IJCAI.

[28]  Harold J. Kushner,et al.  A New Method of Locating the Maximum Point of an Arbitrary Multipeak Curve in the Presence of Noise , 1964 .

[29]  Yaroslav D. Sergeyev,et al.  Global Search Based on Efficient Diagonal Partitions and a Set of Lipschitz Constants , 2006, SIAM J. Optim..

[30]  Y. Sergeyev Efficient Strategy for Adaptive Partition of N-Dimensional Intervals in the Framework of Diagonal Algorithms , 2000 .

[31]  Michel Verhaegen,et al.  A sequential Monte Carlo approach to Thompson sampling for Bayesian optimization , 2016, 1604.00169.

[32]  A. G. Sukharev Optimal strategies of the search for an extremum , 1971 .

[33]  Kazuomi Yamamoto,et al.  Efficient Optimization Design Method Using Kriging Model , 2005 .

[34]  Seungjin Choi,et al.  Clustering-Guided Gp-Ucb for Bayesian Optimization , 2018, 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[35]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

[36]  Kirthevasan Kandasamy,et al.  Parallelised Bayesian Optimisation via Thompson Sampling , 2018, AISTATS.

[37]  David Ginsbourger,et al.  Noisy Expected Improvement and on-line computation time allocation for the optimization of simulators with tunable fidelity , 2010 .

[38]  Garrett M Morris,et al.  Bayesian optimization for conformer generation , 2018, Journal of Cheminformatics.

[39]  Nathalie Bartoli,et al.  An adaptive feasibility approach for constrained bayesian optimization with application in aircraft design , 2018 .

[40]  Antanas Žilinskas,et al.  A statistical model for global optimization by means of select and clone , 2000 .

[41]  Jasper Snoek,et al.  Bayesian Optimization with Unknown Constraints , 2014, UAI.

[42]  Victor Picheny,et al.  Comparison of Kriging-based algorithms for simulation optimization with heterogeneous noise , 2017, Eur. J. Oper. Res..

[43]  H. Kushner A versatile stochastic model of a function of unknown and time varying form , 1962 .

[44]  Swati Aggarwal,et al.  Hyperparameter Optimization Using Sustainable Proof of Work in Blockchain , 2020, Frontiers in Blockchain.

[45]  Antanas Žilinskas,et al.  A hybrid of Bayesian approach based global search with clustering aided local refinement , 2019, Commun. Nonlinear Sci. Numer. Simul..

[46]  Alán Aspuru-Guzik,et al.  Phoenics: A Bayesian Optimizer for Chemistry , 2018, ACS central science.

[47]  Jerome Sacks,et al.  Designs for Computer Experiments , 1989 .

[48]  Matthew W. Hoffman,et al.  A General Framework for Constrained Bayesian Optimization using Information-based Search , 2015, J. Mach. Learn. Res..

[49]  A. Zilinskas,et al.  Algorithm AS 133: Optimization of One-Dimensional Multimodal Functions , 1978 .

[50]  Yuta Suzuki,et al.  Automated crystal structure analysis based on blackbox optimisation , 2020, npj Computational Materials.

[51]  Michael James Sasena,et al.  Flexibility and efficiency enhancements for constrained global design optimization with kriging approximations. , 2002 .

[52]  Stephen Tyree,et al.  Exact Gaussian Processes on a Million Data Points , 2019, NeurIPS.

[53]  Romas Baronas,et al.  Multi-objective optimization and decision visualization of batch stirred tank reactor based on spherical catalyst particles , 2019, Nonlinear Analysis: Modelling and Control.

[54]  A. ilinskas,et al.  One-Dimensional global optimization for observations with noise , 2005 .

[55]  Nando de Freitas,et al.  Taking the Human Out of the Loop: A Review of Bayesian Optimization , 2016, Proceedings of the IEEE.

[56]  Robert B. Gramacy,et al.  Massively parallel approximate Gaussian process regression , 2013, SIAM/ASA J. Uncertain. Quantification.

[57]  Marc Peter Deisenroth,et al.  Efficiently sampling functions from Gaussian process posteriors , 2020, ICML.

[58]  Demis Hassabis,et al.  Mastering the game of Go with deep neural networks and tree search , 2016, Nature.

[59]  Svetha Venkatesh,et al.  Exploration Enhanced Expected Improvement for Bayesian Optimization , 2018, ECML/PKDD.

[60]  R. A. Miller,et al.  Sequential kriging optimization using multiple-fidelity evaluations , 2006 .

[61]  Liesbet Geris,et al.  Bayesian Multiobjective Optimisation With Mixed Analytical and Black-Box Functions: Application to Tissue Engineering , 2019, IEEE Transactions on Biomedical Engineering.

[62]  L. Cornejo-Bueno,et al.  Bayesian optimization of a hybrid system for robust ocean wave features prediction , 2018, Neurocomputing.

[63]  David Volent Lindberg,et al.  Optimization Under Constraints by Applying an Asymmetric Entropy Measure , 2015 .

[64]  Céline Helbert,et al.  Gaussian process optimization with failures: classification and convergence proof , 2020, Journal of Global Optimization.

[65]  Victor Picheny,et al.  Multiobjective optimization using Gaussian process emulators via stepwise uncertainty reduction , 2013, Statistics and Computing.

[66]  A. Zilinskas,et al.  Two algorithms for one-dimensional multimodai minimization , 1981 .

[67]  A. Žilinskas,et al.  One-Dimensional P-Algorithm with Convergence Rate O(n−3+δ) for Smooth Functions , 2000 .

[68]  Matthias Poloczek,et al.  Advances in Bayesian Optimization with Applications in Aerospace Engineering , 2018 .

[69]  A. Zilinskas,et al.  Global optimization based on a statistical model and simplicial partitioning , 2002 .

[70]  D. Ginsbourger,et al.  Dealing with asynchronicity in parallel Gaussian Process based global optimization , 2010 .

[71]  Antanas Žilinskas,et al.  A hybrid of the simplicial partition-based Bayesian global search with the local descent , 2020, Soft Comput..

[72]  Andreas Krause,et al.  Joint Optimization and Variable Selection of High-dimensional Gaussian Processes , 2012, ICML.

[73]  Karen Willcox,et al.  Lookahead Bayesian Optimization with Inequality Constraints , 2017, NIPS.

[74]  Cheng Li,et al.  High Dimensional Bayesian Optimization using Dropout , 2018, IJCAI.

[75]  E. Vázquez,et al.  Convergence properties of the expected improvement algorithm with fixed mean and covariance functions , 2007, 0712.3744.

[76]  Peter Auer,et al.  Using Confidence Bounds for Exploitation-Exploration Trade-offs , 2003, J. Mach. Learn. Res..

[77]  Caslav Ilic,et al.  Surrogate-Based Aerodynamic Shape Optimization of a Wing-Body Transport Aircraft Configuration , 2015 .

[78]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[79]  Matthew W. Hoffman,et al.  Predictive Entropy Search for Bayesian Optimization with Unknown Constraints , 2015, ICML.

[80]  James M. Calvin An Adaptive Univariate Global Optimization Algorithm and Its Convergence Rate under the Wiener Measure , 2011, Informatica.

[81]  Zi Wang,et al.  Max-value Entropy Search for Efficient Bayesian Optimization , 2017, ICML.

[82]  Antanas Zilinskas,et al.  Axiomatic approach to statistical models and their use in multimodal optimization theory , 1982, Math. Program..

[83]  D. Ginsbourger,et al.  A benchmark of kriging-based infill criteria for noisy optimization , 2013, Structural and Multidisciplinary Optimization.

[84]  E. Novak Deterministic and Stochastic Error Bounds in Numerical Analysis , 1988 .

[85]  C. D. Perttunen,et al.  Lipschitzian optimization without the Lipschitz constant , 1993 .

[86]  Klaus Ritter,et al.  Approximation and optimization on the Wiener space , 1990, J. Complex..

[87]  Roman Garnett,et al.  Bayesian optimization for sensor set selection , 2010, IPSN '10.

[88]  Antanas Zilinskas On the worst-case optimal multi-objective global optimization , 2013, Optim. Lett..

[89]  Matthias Poloczek,et al.  Scalable Global Optimization via Local Bayesian Optimization , 2019, NeurIPS.

[90]  Matthew W. Hoffman,et al.  An Entropy Search Portfolio for Bayesian Optimization , 2014, ArXiv.

[91]  A. ilinskas Axiomatic characterization of a global optimization algorithm and investigation of its search strategy , 1985 .

[92]  Antanas Zilinskas,et al.  Selection of a covariance function for a Gaussian random field aimed for modeling global optimization problems , 2019, Optim. Lett..

[93]  D. Ginsbourger,et al.  Towards GP-based optimization with finite time horizon , 2009 .

[94]  Andrew Gordon Wilson,et al.  Scaling Gaussian Process Regression with Derivatives , 2018, NeurIPS.

[95]  Matthias Poloczek,et al.  Bayesian Optimization with Gradients , 2017, NIPS.

[96]  Michael L. Stein,et al.  Maximum Likelihood Estimation for a Smooth Gaussian Random Field Model , 2017, SIAM/ASA J. Uncertain. Quantification.

[97]  Joshua D. Knowles,et al.  Initialization of Bayesian Optimization Viewed as Part of a Larger Algorithm Portfolio , 2017 .

[98]  Udo von Toussaint,et al.  Global Optimization Employing Gaussian Process-Based Bayesian Surrogates† , 2018, Entropy.

[99]  Shipra Agrawal,et al.  Analysis of Thompson Sampling for the Multi-armed Bandit Problem , 2011, COLT.

[100]  James M. Calvin Consistency of a myopic Bayesian algorithm for one-dimensional global optimization , 1993, J. Glob. Optim..

[101]  Konrad Wegener,et al.  Self-optimizing grinding machines using Gaussian process models and constrained Bayesian optimization , 2020, The International Journal of Advanced Manufacturing Technology.

[102]  A. Basudhar,et al.  Constrained efficient global optimization with support vector machines , 2012, Structural and Multidisciplinary Optimization.

[103]  A. Yaglom Correlation Theory of Stationary and Related Random Functions I: Basic Results , 1987 .

[104]  Antonio Candelieri,et al.  Sequential model based optimization of partially defined functions under unknown constraints , 2019, J. Glob. Optim..

[105]  E. Novak,et al.  Tractability of Multivariate Problems Volume II: Standard Information for Functionals , 2010 .

[106]  Wei-Liem Loh,et al.  Estimating structured correlation matrices in smooth Gaussian random field models , 2000 .

[107]  Marc Toussaint,et al.  Advancing Bayesian Optimization: The Mixed-Global-Local (MGL) Kernel and Length-Scale Cool Down , 2016, ArXiv.

[108]  Cheng Li,et al.  Regret for Expected Improvement over the Best-Observed Value and Stopping Condition , 2017, ACML.

[109]  James M. Calvin,et al.  On convergence rate of a rectangular partition based global optimization algorithm , 2018, J. Glob. Optim..

[110]  James M. Calvin,et al.  Adaptive approximation of the minimum of Brownian motion , 2017, J. Complex..

[111]  Hang Lei,et al.  Hyperparameter Optimization for Machine Learning Models Based on Bayesian Optimization , 2019 .

[112]  Stephen J. Roberts,et al.  Optimization, fast and slow: optimally switching between local and Bayesian optimization , 2018, ICML.

[113]  Julius Zilinskas,et al.  Improved scheme for selection of potentially optimal hyper-rectangles in DIRECT , 2017, Optimization Letters.

[114]  A. Žilinskas,et al.  An estimate of the Wiener process parameter , 1978 .

[115]  Chun-Liang Li,et al.  High Dimensional Bayesian Optimization via Restricted Projection Pursuit Models , 2016, AISTATS.

[116]  Joshua D. Knowles,et al.  Multiobjective Optimization on a Budget of 250 Evaluations , 2005, EMO.

[117]  James M. Calvin,et al.  On a Global Optimization Algorithm for Bivariate Smooth Functions , 2014, J. Optim. Theory Appl..

[118]  Peter I. Frazier,et al.  Multi-Step Bayesian Optimization for One-Dimensional Feasibility Determination , 2016, ArXiv.

[119]  K. Hukushima,et al.  Bayesian optimization for computationally extensive probability distributions , 2018, PloS one.

[120]  Peter I. Frazier,et al.  Discretization-free Knowledge Gradient Methods for Bayesian Optimization , 2017, ArXiv.

[121]  Qingfu Zhang,et al.  A multiobjective optimization based framework to balance the global exploration and local exploitation in expensive optimization , 2015, J. Glob. Optim..

[122]  Jieun Lee,et al.  Bayesian Optimization-Based Global Optimal Rank Selection for Compression of Convolutional Neural Networks , 2020, IEEE Access.

[123]  Ola Engkvist,et al.  Randomized SMILES strings improve the quality of molecular generative models , 2019, Journal of Cheminformatics.

[124]  Adam D. Bull,et al.  Convergence Rates of Efficient Global Optimization Algorithms , 2011, J. Mach. Learn. Res..

[125]  Frank Hutter,et al.  Maximizing acquisition functions for Bayesian optimization , 2018, NeurIPS.

[126]  Elad Gilboa,et al.  Scaling Multidimensional Gaussian Processes using Projected Additive Approximations , 2013, ICML.

[127]  J. L. Maryak,et al.  Bayesian Heuristic Approach to Discrete and Global Optimization , 1999, Technometrics.

[128]  Robert B. Gramacy,et al.  Optimization Under Unknown Constraints , 2010, 1004.4027.

[129]  Régis Duvigneau,et al.  A classification approach to efficient global optimization in presence of non-computable domains , 2018 .

[130]  M. Sheikholeslami,et al.  A novel Bayesian optimization for flow condensation enhancement using nanorefrigerant: A combined analytical and experimental study , 2020 .

[131]  Julius Žilinskas,et al.  P-algorithm based on a simplicial statistical model of multimodal functions , 2010 .

[132]  Dept. of Physics,et al.  Estimating the $K$ function of a point process with an application to cosmology , 2000, physics/0006047.

[133]  Yaroslav D. Sergeyev,et al.  Numerical infinities and infinitesimals: Methodology, applications, and repercussions on two Hilbert problems , 2017 .

[134]  Jos'e Miguel Hern'andez-Lobato,et al.  Constrained Bayesian Optimization for Automatic Chemical Design , 2017 .

[135]  Philipp Hennig,et al.  Entropy Search for Information-Efficient Global Optimization , 2011, J. Mach. Learn. Res..

[136]  Michael L. Stein,et al.  Interpolation of spatial data , 1999 .

[137]  James M. Calvin,et al.  On Convergence of a P-Algorithm Based on a Statistical Model of Continuously Differentiable Functions , 2001, J. Glob. Optim..

[138]  Cheng Soon Ong,et al.  Multivariate spearman's ρ for aggregating ranks using copulas , 2016 .

[139]  Cheng Li,et al.  High Dimensional Bayesian Optimization with Elastic Gaussian Process , 2017, ICML.

[140]  Marc Toussaint,et al.  Bayesian Functional Optimization , 2018, AAAI.

[141]  Y. D. Sergeyev,et al.  Global Optimization with Non-Convex Constraints - Sequential and Parallel Algorithms (Nonconvex Optimization and its Applications Volume 45) (Nonconvex Optimization and Its Applications) , 2000 .

[142]  J. Mockus,et al.  The Bayesian approach to global optimization , 1989 .

[143]  Andrew Gordon Wilson,et al.  Scalable Log Determinants for Gaussian Process Kernel Learning , 2017, NIPS.

[144]  János D. Pintér,et al.  Global optimization in action , 1995 .

[145]  Rabiatul Adwiya,et al.  Perancangan Permainan Edukasi Peduli Jajanan Sehat , 2017 .

[146]  Thomas J. Santner,et al.  Design and analysis of computer experiments , 1998 .

[147]  A. Zilinskas,et al.  On an Asymptotic Property of a Simplicial Statistical Model of Global Optimization , 2015 .

[148]  Victor Picheny,et al.  Bayesian optimization under mixed constraints with a slack-variable augmented Lagrangian , 2016, NIPS.

[149]  Byung Joon Lee,et al.  Exploring multi-stage shape optimization strategy of multi-body geometries using Kriging-based model and adjoint method , 2012 .

[150]  Farrokh Mistree,et al.  Kriging Models for Global Approximation in Simulation-Based Multidisciplinary Design Optimization , 2001 .