The Knowledge-Gradient Policy for Correlated Normal Beliefs

By Peter I. Frazier, Warrren B Powell, Savas Dayanik. 2009

466 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Ocean Engineering

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Citations in the corpus

Hyper-Parameter Optimization: A Review of Algorithms and Applications (2020, background): “In addition to improvement-based policies, knowledge gradient function (Frazier et al., 2009), entropy search function (Hennig and Schuler, 2012), and predictive entropy search function (Hernández-Lobato et al., 2014) have recently been developed to enhance performance over different applications.”
A Tutorial on Thompson Sampling (2017, background): “The knowledge gradient [61, 62] and information-directed sampling [50] are alternative algorithms that attempt to reason more carefully about the value of information acquired by sampling an action.”
Monte Carlo sampling-based methods for stochastic optimization (2014, unknown): “[77, 78], Huang et al.”
Customer Acquisition via Display Advertising Using Multi-Armed Bandit Experiments (2017, methodology): “A family of methods known as expected value of information gained and knowledge gradient optimize this extra optimal stopping problem in a bandit setting (Chick and Gans 2009; Chick and Inoue 2001; Chick et al. 2010; Frazier et al. 2009; Powell 2011).”
A unified framework for stochastic optimization (2019, methodology): “This is rare instance of a problem where we can actually compute an ptimal policy. There is a long history in the development of optimal conrol, summarized by many books including ( Kirk, 2004; Sethi Thompson, 20 0 0; Sontag, 1998; Stengel, 1986 ), and Lewis nd Vrabie (2012) .”
A Tutorial on Bayesian Optimization (2018, methodology): “This provides a small performance benefit in the standard BayesOpt problem with noise-free evaluations (Frazier et al., 2009),”
Multi-Information Source Optimization (2016, methodology): “We begin its computation by sorting the entries of ¯ µ n and ¯ σ n ( ‘, x ) in parallel by ascending ¯ σ n ( ‘, x )- value; if multiple entries have the same ¯ σ n ( ‘, x ), we only keep the entry with largest value in ¯ µ n and discard all others, since they are dominated [Frazier et al., 2009].”
Bayesian Optimization in a Billion Dimensions via Random Embeddings (2013, methodology): “…community has increasingly used Bayesian optimization (Rasmussen, 2003; Brochu et al., 2007; Martinez-Cantin et al., 2007; Lizotte et al., 2007; Frazier et al., 2009; Azimi et al., 2010; Hamze et al., 2011; Azimi et al., 2011; Bergstra et al., 2011; Gramacy & Polson, 2011; Denil et al., 2012;…”
Simulation optimization: a review of algorithms and applications (2014, background): “ response surface, trust region [32] 2011 GR Golden region search [106] 2011 SNM Direct search (Nelder-Mead) [31] 2012 DiceOptim Global response surface [169] 2012 Discrete KG Global response surface [57] 2009 COMPASS Neighborhood search (integer-ordered problems) [206] 2010 R-SPLINE Neighborhood se”
Bayesian Optimization is Superior to Random Search for Machine Learning Hyperparameter Tuning: Analysis of the Black-Box Optimization Challenge 2020 (2021, methodology): “Using this surrogate model, an acquisition function is used to determine the most promising point to evaluate next, where popular options include expected improvement (EI) [35], knowledge gradient (KG) [18], and entropy search (ES) [31].”
The Parallel Knowledge Gradient Method for Batch Bayesian Optimization (2016, methodology): “Our method is also closely related to the knowledge gradient(KG) method [7, 15] for the non-batch (sequential) setting, which chooses the Bayes-optimal point t evaluate if only one iteration is left [15], and the final solution that we choose is not restricted to be one of the points we evaluate.”
Convergence Rates of Efficient Global Optimization Algorithms (2011, background): “ﬃcient global optimization when data is obtained under noise. While expected improvement is designed for noiseless data, heuristic modiﬁcations for noise have been proposed by Huang et al. (2006) and Frazier et al. (2009), among others. Theoretical results are available for the related bandit proble”
BoTorch: Programmable Bayesian Optimization in PyTorch (2019, background): “As was done in the proof of Theorem 4 of [24], we define the event: HA = { αKG(x;μ∞,Σ∞) > 0, x ∈ A } ∩ { αKG(x;μ∞,Σ∞) = 0, x 6∈ A } .”
Static and Dynamic Values of Computation in MCTS (2020, methodology): “The maximum of this variable, i.e. maxEQ∗0 |ω1:tΩ[Q ∗ 0|ω1:tΩ], is a piecewise linear function in Oωt+1 and thus its expectation can be computed exactly in O(m2 logm) as shown in Frazier, Powell, and Dayanik (2009).”