Hybrid Batch Bayesian Optimization

By Javad Azimi, Ali Jalali, Xiaoli Z. Fern. 2012

77 citations recorded by the source corpus.

Bayesian Optimization aims at optimizing an unknown non-convex/concave function that is costly to evaluate. We are interested in application scenarios where concurrent function evaluations are possible. Under such a setting, BO could choose to either sequentially evaluate the function, one input at a time and wait for the output of the function before making the next selection, or evaluate the function at a batch of multiple inputs at once. These two different settings are commonly referred to as the sequential and batch settings of Bayesian Optimization. In general, the sequential setting leads to better optimization performance as each function evaluation is selected with more information, whereas the batch setting has an advantage in terms of the total experimental time (the number of iterations). In this work, our goal is to combine the strength of both settings. Specifically, we systematically analyze Bayesian optimization using Gaussian process as the posterior estimator and provide a hybrid algorithm that, based on the current state, dynamically switches between a sequential policy and a batch policy with variable batch sizes. We provide theoretical justification for our algorithm and present experimental results on eight benchmark BO problems. The results show that our method achieves substantial speedup (up to %78) compared to a pure sequential policy, without suffering any significant performance loss.

Subfields: Artificial Intelligence, Computer Networks and Communications, Management Science and Operations Research

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Citations in the corpus

Taking the Human Out of the Loop: A Review of Bayesian Optimization (2016, background): “In academia, it is impacting a wide range of areas, including interactive user interfaces [26], robotics [101], [110], environmental monitoring [106], information extraction [157], combinatorial optimization [79], [158], automatic machine learning [16], [72], [143], [148], [151], sensor networks [55”
Heteroscedastic Treed Bayesian Optimisation (2014, background): “, 2013), experimental design (Azimi et al., 2012), and reinforcement learning (Brochu et al.”
UvA-DARE (Digital Academic Repository) Bayesian Optimization in High Dimensions via Random Embeddings (2013, unknown): “In recent years, the artiﬁcial intelligence community has increasingly used Bayesian optimization; see for example [ Martinez–Cantin et al. , 2009; Brochu et al. , 2009; Srini-vas et al. , 2010; Hoffman et al. , 2011; Lizotte et al. , 2011; Azimi et al. , 2012 ] .”
An Entropy Search Portfolio for Bayesian Optimization (2014, methodology): “…of these techniques include interactive user-interfaces [6, 4], robotics [18, 21], environmental monitoring [20], information extraction [33], combinatorial optimization [16, 34], sensor networks [10, 28], adaptive Monte Carlo [19, 32], experimental design [1], and reinforcement learning [5].”
Bayesian Optimization in a Billion Dimensions via Random Embeddings (2013, background): “…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; Mahendran et al., 2012; Azimi et al., 2012; Hen-nig & Schuler, 2012; Marchant & Ramos, 2012).”
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”
Batch Bayesian Optimization via Local Penalization (2015, methodology): “[Schonlau et al., 1998] and [Contal et al., 2013], Pred is used in cases when the model is used to generate ‘fake’ batch observations as in [Azimi et al., 2012], SM identi-ﬁes the simulating and matching method [Azimi et al., 2010] and LP stands for our local penalization method.”
Bayesian Optimization with Inequality Constraints (2014, background): “Parallelizing Bayesian optimization is an active research area (Azimi et al., 2010a; 2012; Snoek et al., 2012).”
On Kernelized Multi-armed Bandits (2017, methodology): “We consider 2 well-known synthetic benchmark functions for Bayesian Optimization: Rosenbrock and Hartman 3 (see Azimi et al. (2012) for exact analytical expressions).”