Bayesian Multi-Scale Optimistic Optimization

By Ziyun Wang, Babak Shakibi, Lingzi Jin, Nando de Freitas. 2014

95 citations recorded by the source corpus.

Bayesian optimization is a powerful global optimization technique for expensive black-box functions. One of its shortcomings is that it requires auxiliary optimization of an acquisition function at each iteration. This auxiliary optimization can be costly and very hard to carry out in practice. Moreover, it creates serious theoretical concerns, as most of the convergence results assume that the exact optimum of the acquisition function can be found. In this paper, we introduce a new technique for efficient global optimization that combines Gaussian process confidence bounds and treed simultaneous optimistic optimization to eliminate the need for auxiliary optimization of acquisition functions. The experiments with global optimization benchmarks and a novel application to automatic information extraction demonstrate that the resulting technique is more efficient than the two approaches from which it draws inspiration. Unlike most theoretical analyses of Bayesian optimization with Gaussian processes, our finite-time convergence rate proofs do not require exact optimization of an acquisition function. That is, our approach eliminates the unsatisfactory assumption that a difficult, potentially NP-hard, problem has to be solved in order to obtain vanishing regret rates.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Management Science and Operations Research

How researchers see this paper

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

In Artificial Intelligence

In Computational Theory and Mathematics

In Management Science and Operations Research

Citations in the corpus

Taking the Human Out of the Loop: A Review of Bayesian Optimization (2016, neutral): “A natural choice for the prior distribution is a product of K beta distributions: as this is the conjugate prior to the Bernoulli likelihood, and it leads to efﬁcient posterior updating.”
Learning to Learn for Global Optimization of Black Box Functions (2016, background): “It also raises some theoretical concerns [Wang et al., 2014].”
Optimization as Estimation with Gaussian Processes in Bandit Settings (2015, background): “For example, one can combine GP-UCB with hierarchical partitioning of the input space [42, 19], which only needs to compute the acquisition function values on selected points and does not require the optimization of acquisition function.”
Sample-Efficient Neural Architecture Search by Learning Action Space (2019, unknown): “Consistent with [28], our results in Fig.”
Learning to Learn without Gradient Descent by Gradient Descent (2016, unknown): “It also raises some theoretical concerns (Wang et al., 2014).”
Theoretical Analysis of Bayesian Optimisation with Unknown Gaussian Process Hyper-Parameters (2014, background): “Bayesian optimisation has become an important area of research and development in the field of machine learning, as evidenced by recent media coverage [8] and a blossoming range of applications to interactive user-interfaces [4], robotics [16, 19], environmental monitoring [18], information extracti”
Constrained Bayesian Optimization for Automatic Chemical Design (2017, methodology): “ations beyond hyperparameter tuning include A/B testing [58, 101, 13], environmental monitoring and sensor networks [115, 26, 74], Recommender systems [64, 13, 123], Natural Language Processing (NLP) [126, 129] and Statistical Machine Translation (SMT) [4], Robotics and Reinforcement Learning [67, 7”
Heteroscedastic Treed Bayesian Optimisation (2014, background): “For a more detailed description as well as the code of the function, please refer to Wang et al. (2014b).”
An Entropy Search Portfolio for Bayesian Optimization (2014, methodology): “More recently a wide variety of more advanced techniques have been proposed which include Bayesian upper conﬁdence bounds [28, 8, 33] and information-theoretic approaches [31, 11].”