The Bayesian approach to global optimization

By Jonas Mockus. 1989

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Citations in the corpus

Learning to Learn for Global Optimization of Black Box Functions (2016, methodology): “Also the posterior expected improvement used within LEI can be easily computed Močkus [1982] and differentiated as well.”
A Tutorial on Bayesian Optimization of Expensive Cost Functions, with Application to Active User Modeling and Hierarchical Reinforcement Learning (2010, background): “…the risk (defined as the expected deviation from the global minimum at a fixed point x); and (ii) conditional variance converges to zero (or appropriate positive minimum value in the presence of noise) if and only if the distance to the nearest observation is zero [Močkus, 1982, Močkus, 1994].”
Parallelizing Exploration-Exploitation Tradeoffs with Gaussian Process Bandit Optimization (2012, methodology): “We compare it with four alternatives: (1) The strictly sequential GP-UCB algorithm (B = 1); (2) NRB-UCB, an approach that simply picks the maximizer of the GP-UCB score B times; (3) NTB-UCB, an approach that picks the top B scores according to the GP-UCB criterion; (4) A state of the art algorithm f”
Information-Theoretic Regret Bounds for Gaussian Process Optimization in the Bandit Setting (2009, methodology): “Several heuristics for trading oﬀ exploration and exploitation in GP optimization have been proposed (such as Expected Improvement, Mockus et al. 1978, and Most Probable Improvement, Mockus 1989) and successfully applied in practice ( c.f. , Lizotte et al. 2007).”
Sequential design of computer experiments for the estimation of a probability of failure (2010, methodology): “This kind of strategy, sometimes called myopic, has been successfully applied in the field of Bayesian global optimization (Mockus et al., 1978; Mockus, 1989), yielding the famous expected improvement criterion later popularized in the Efficient Global Optimization (EGO) algorithm of Jones et al.…”
Heteroscedastic Treed Bayesian Optimisation (2014, background): “Although many acquisition strategies have been proposed (see for example Močkus (1982); Jones (2001); Hoffman et al. (2011); Hennig and Schuler (2012); Snoek et al. (2012); Hoffman et al. (2014); Wang et al. (2014a); Shahriari et al. (2014)), the expected improvement (EI) criterion remains a…”
Global optimization based on a statistical model and simplicial partitioning (2002, background): “A review of global optimization based on multidimensional statistical models may be found in [8,11].”
Exponential Regret Bounds for Gaussian Process Bandits with Deterministic Observations (2012, background): “We refer the reader to (Močkus, 1982; Schonlau et al., 1998; Gramacy et al., 2004; Brochu et al., 2007; Lizotte, 2008; Martinez–Cantin et al., 2009; Garnett et al., 2010) for practical examples.”
Quantile-Based Optimization of Noisy Computer Experiments With Tunable Precision (2013, unknown): “It has been shown (Mockus (1988) followed by Ginsbourger and Le Riche (2010)) that taking into account the ﬁnite budget may modify the optimization strategy and improve signiﬁcantly its eﬃciency.”
Application of Bayesian approach to numerical methods of global and stochastic optimization (1994, methodology): “It seems reasonable to replace Kolmogorov's consistency conditions by the following three assumptions: (i) Continuity of risk function (8) (ii) Convergence of method (9) to a global minimum of any continuous function (iii) Simplicity of expressions for/zn(x) and o-n(x) Then method (9) can be express”
BayesOpt: a Bayesian optimization library for nonlinear optimization, experimental design and bandits (2014, background): “Bayesian optimization (Mockus, 1989; Brochu et al., 2010) is a special case of nonlinear optimization where the algorithm decides which point to explore next based on the analysis of a distribution over functions P ( f ), for example a Gaussian process or other surrogate model .”