Exploration Enhanced Expected Improvement for Bayesian Optimization

Berk, Julian; Nguyen, Vu; Gupta, Sunil; Rana, Santu; Venkatesh, Svetha

doi:10.1007/978-3-030-10928-8_37

Cited by 36 publications

(26 citation statements)

References 8 publications

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“…EI's deteriorating performance at higher noise levels may indicate that the surrogate model is poorer at representing the noisy function, leading to insufficient exploration. This is in contrast to the more exploratory UCB, which over-explores in the noise-free case [3]. It would be interesting to investigate BO strategies for optimisation in the presence of noise.…”

Section: Resultsmentioning

confidence: 99%

How Bayesian should Bayesian optimisation be?

Ath

Everson

Fieldsend

2021

Proceedings of the Genetic and Evolutionary Computation Conference Companion

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Bayesian optimisation (BO) uses probabilistic surrogate modelsusually Gaussian processes (GPs) -for the optimisation of expensive black-box functions. At each BO iteration, the GP hyperparameters are fit to previously-evaluated data by maximising the marginal likelihood. However, this fails to account for uncertainty in the hyperparameters themselves, leading to overconfident model predictions. This uncertainty can be accounted for by taking the Bayesian approach of marginalising out the model hyperparameters. We investigate whether a fully-Bayesian treatment of the Gaussian process hyperparameters in BO (FBBO) leads to improved optimisation performance. Since an analytic approach is intractable, we compare FBBO using three approximate inference schemes to the maximum likelihood approach, using the Expected Improvement (EI) and Upper Confidence Bound (UCB) acquisition functions paired with ARD and isotropic Matérn kernels, across 15 well-known benchmark problems for 4 observational noise settings. FBBO using EI with an ARD kernel leads to the best performance in the noise-free setting, with much less difference between combinations of BO components when the noise is increased. FBBO leads to over-exploration with UCB, but is not detrimental with EI. Therefore, we recommend that FBBO using EI with an ARD kernel as the default choice for BO. CCS CONCEPTS• Theory of computation → Gaussian processes; Mathematical optimization; • Mathematics of computing → Bayesian computation.

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Section: Resultsmentioning

confidence: 99%

How Bayesian should Bayesian optimisation be?

Ath

Everson

Fieldsend

2021

Proceedings of the Genetic and Evolutionary Computation Conference Companion

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“…We concentrate on CB (LCB in particular) because a simple amendment of it gives very satisfactory results (see Section IV). Berk et al [18] indicate that EI is prone to detecting a local rather than a global optimum. A common heuristic is that EI is not appropriate for noisy problems because when noise is present, the optimal observation may not correspond to the true optimal function value.…”

Section: The Acquisition Functionmentioning

confidence: 99%

Improved Gaussian Process Acquisition for Targeted Bayesian Optimization

Mitic¹

2021

IJMO

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A black-box optimization problem is considered, in which the function to be optimized can only be expressed in terms of a complicated stochastic algorithm that takes a long time to evaluate. The value returned is required to be sufficiently near to a target value, and uses data that has a significant noise component. Bayesian Optimization with an underlying Gaussian Process is used as an optimization solution, and its effectiveness is measured in terms of the number of function evaluations required to attain the target. To improve results, a simple modification of the Gaussian Process ‘Lower Confidence Bound’ (LCB) acquisition function is proposed. The expression used for the confidence bound is squared in order to better comply with the target requirement. With this modification, much improved results compared to random selection methods and to other commonly used acquisition functions are obtained.

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“…In contrast, Sequential Model-Based Optimization (SMBO) (Jones et al 1998) takes advantage of the previous search trajectory. Several benchmarks (Hutter et al 2013;Bischl et al 2017;Berk et al 2018) demonstrate the superiority of MBO over grid and random search as well as evolutionary approaches. In the classical approach, Gaussian process regression, also called Kriging, is used as its regression model (Snoek et al 2012).…”

Section: Hyper-parameter Tuning Algorithmsmentioning

confidence: 99%

MODES: model-based optimization on distributed embedded systems

et al. 2021

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The predictive performance of a machine learning model highly depends on the corresponding hyper-parameter setting. Hence, hyper-parameter tuning is often indispensable. Normally such tuning requires the dedicated machine learning model to be trained and evaluated on centralized data to obtain a performance estimate. However, in a distributed machine learning scenario, it is not always possible to collect all the data from all nodes due to privacy concerns or storage limitations. Moreover, if data has to be transferred through low bandwidth connections it reduces the time available for tuning. Model-Based Optimization (MBO) is one state-of-the-art method for tuning hyper-parameters but the application on distributed machine learning models or federated learning lacks research. This work proposes a framework $$\textit{MODES}$$ MODES that allows to deploy MBO on resource-constrained distributed embedded systems. Each node trains an individual model based on its local data. The goal is to optimize the combined prediction accuracy. The presented framework offers two optimization modes: (1) $$\textit{MODES}$$ MODES -B considers the whole ensemble as a single black box and optimizes the hyper-parameters of each individual model jointly, and (2) $$\textit{MODES}$$ MODES -I considers all models as clones of the same black box which allows it to efficiently parallelize the optimization in a distributed setting. We evaluate $$\textit{MODES}$$ MODES by conducting experiments on the optimization for the hyper-parameters of a random forest and a multi-layer perceptron. The experimental results demonstrate that, with an improvement in terms of mean accuracy ($$\textit{MODES}$$ MODES -B), run-time efficiency ($$\textit{MODES}$$ MODES -I), and statistical stability for both modes, $$\textit{MODES}$$ MODES outperforms the baseline, i.e., carry out tuning with MBO on each node individually with its local sub-data set.

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Exploration Enhanced Expected Improvement for Bayesian Optimization

Cited by 36 publications

References 8 publications

How Bayesian should Bayesian optimisation be?

How Bayesian should Bayesian optimisation be?

Improved Gaussian Process Acquisition for Targeted Bayesian Optimization

MODES: model-based optimization on distributed embedded systems

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