scholarly journals Bayesian Optimization using Pseudo-Points

2020 ◽  
Author(s):  
Chao Qian ◽  
Hang Xiong ◽  
Ke Xue
Keyword(s):  
Parameter Tuning ◽  
Black Box ◽  
Bayesian Optimization ◽  
Confidence Bound ◽  
Data Points ◽  
Upper Confidence Bound ◽  
Gp Model ◽  
Probability Of Improvement ◽  
And Robotics ◽  
Real World Problems

Bayesian optimization (BO) is a popular approach for expensive black-box optimization, with applications including parameter tuning, experimental design, and robotics. BO usually models the objective function by a Gaussian process (GP), and iteratively samples the next data point by maximizing an acquisition function. In this paper, we propose a new general framework for BO by generating pseudo-points (i.e., data points whose objective values are not evaluated) to improve the GP model. With the classic acquisition function, i.e., upper confidence bound (UCB), we prove that the cumulative regret can be generally upper bounded. Experiments using UCB and other acquisition functions, i.e., probability of improvement (PI) and expectation of improvement (EI), on synthetic as well as real-world problems clearly show the advantage of generating pseudo-points.

scholarly journals Multi-Task Gaussian Process Upper Confidence Bound for Hyperparameter Tuning

2021 ◽  
Author(s):  
Bo Shen ◽  
Raghav Gnanasambandam ◽  
Rongxuan Wang ◽  
Zhenyu Kong
Keyword(s):  
Gaussian Process ◽  
Black Box ◽  
Bayesian Optimization ◽  
Query Point ◽  
Confidence Bound ◽  
Bayesian Optimization Algorithm ◽  
Machine Learning Model ◽  
Step Algorithm ◽  
Upper Confidence Bound ◽  
General Method

In many scientific and engineering applications, Bayesian optimization (BO) is a powerful tool for hyperparameter tuning of a machine learning model, materials design and discovery, etc. BO guides the choice of experiments in a sequential way to find a good combination of design points in as few experiments as possible. It can be formulated as a problem of optimizing a “black-box” function. Different from single-task Bayesian optimization, Multi-task Bayesian optimization is a general method to efficiently optimize multiple different but correlated “black-box” functions. The previous works in Multi-task Bayesian optimization algorithm queries a point to be evaluated for all tasks in each round of search, which is not efficient. For the case where different tasks are correlated, it is not necessary to evaluate all tasks for a given query point. Therefore, the objective of this work is to develop an algorithm for multi-task Bayesian optimization with automatic task selection so that only one task evaluation is needed per query round. Specifically, a new algorithm, namely, multi-task Gaussian process upper confidence bound (MT-GPUCB), is proposed to achieve this objective. The MT-GPUCB is a two-step algorithm, where the first step chooses which query point to evaluate, and the second step automatically selects the most informative task to evaluate. Under the bandit setting, a theoretical analysis is provided to show that our proposed MT-GPUCB is no-regret under some mild conditions. Our proposed algorithm is verified experimentally on a range of synthetic functions as well as real-world problems. The results clearly show the advantages of our query strategy for both design point and task.

scholarly journals Multi-Task Gaussian Process Upper Confidence Bound for Hyperparameter Tuning

2021 ◽  
Author(s):  
Bo Shen ◽  
Raghav Gnanasambandam ◽  
Rongxuan Wang ◽  
Zhenyu Kong
Keyword(s):  
Gaussian Process ◽  
Black Box ◽  
Bayesian Optimization ◽  
Query Point ◽  
Confidence Bound ◽  
Bayesian Optimization Algorithm ◽  
Machine Learning Model ◽  
Step Algorithm ◽  
Upper Confidence Bound ◽  
General Method

In many scientific and engineering applications, Bayesian optimization (BO) is a powerful tool for hyperparameter tuning of a machine learning model, materials design and discovery, etc. BO guides the choice of experiments in a sequential way to find a good combination of design points in as few experiments as possible. It can be formulated as a problem of optimizing a “black-box” function. Different from single-task Bayesian optimization, Multi-task Bayesian optimization is a general method to efficiently optimize multiple different but correlated “black-box” functions. The previous works in Multi-task Bayesian optimization algorithm queries a point to be evaluated for all tasks in each round of search, which is not efficient. For the case where different tasks are correlated, it is not necessary to evaluate all tasks for a given query point. Therefore, the objective of this work is to develop an algorithm for multi-task Bayesian optimization with automatic task selection so that only one task evaluation is needed per query round. Specifically, a new algorithm, namely, multi-task Gaussian process upper confidence bound (MT-GPUCB), is proposed to achieve this objective. The MT-GPUCB is a two-step algorithm, where the first step chooses which query point to evaluate, and the second step automatically selects the most informative task to evaluate. Under the bandit setting, a theoretical analysis is provided to show that our proposed MT-GPUCB is no-regret under some mild conditions. Our proposed algorithm is verified experimentally on a range of synthetic functions as well as real-world problems. The results clearly show the advantages of our query strategy for both design point and task.

scholarly journals Bayesian Optimization for Parameter of Discrete Weibull Regression

2020 ◽  
pp. 1-13
Author(s):  
Adesina, Olumide Sunday ◽  
Onanaye, Adeniyi Samson ◽  
Okewole, Dorcas Modupe
Keyword(s):  
Count Data ◽  
Optimization Problem ◽  
Likelihood Function ◽  
Bayesian Optimization ◽  
Confidence Bound ◽  
Mcmc Algorithm ◽  
Weibull Regression ◽  
Weibull Regression Model ◽  
Upper Confidence Bound ◽  
Probability Of Improvement

This study aim at optimizing the parameter θ of Discrete Weibull (DW) regression obtained by maximizing the likelihood function. Also to examine the strength of three acquisition functions used in solving auxiliary optimization problem. The choice of Discrete Weibull regression model among other models for fitting count data is due to its robustness in fitting count data. Count data of hypertensive patients visits to the doctor was obtained at Medicare Clinics Ota, Nigeria, and was used for the analysis. First, parameter θ  and β  were obtained using Metropolis Hasting Monte Carlo Markov Chain (MCMC) algorithm. Then Bayesian optimization was used to optimize the parameter the likelihood function of DW regression, given β to examine what θ would be, and making the likelihood function of DW the objective function. Upper confidence bound (UCB), Expectation of Improvement (EI), and probability of Improvement (PI) were used as acquisition functions. Results showed that fitting Bayesian DW regression to the data, there is significant relationship between the response variable, β and the covariate. On implementing Bayesian optimization to obtain parameter new parameter θ of discrete Weibull regression using the known β, the results showed promising applicability of the technique to the model, and found that EI fits the data better relative to PI and UCB in terms of accuracy and speed.

scholarly journals Multi-fidelity Gaussian Process Bandit Optimisation

2019 ◽  
Vol 66 ◽  
pp. 151-196 ◽  
Author(s):  
Kirthevasan Kandasamy ◽  
Gautam Dasarathy ◽  
Junier Oliva ◽  
Jeff Schneider ◽  
Barnabás Póczos
Keyword(s):  
Computer Simulation ◽  
Theoretical Analysis ◽  
Gaussian Process ◽  
Target Function ◽  
Black Box ◽  
Confidence Bound ◽  
Bandit Problem ◽  
Single Function ◽  
Novel Method ◽  
Upper Confidence Bound

In many scientific and engineering applications, we are tasked with the maximisation of an expensive to evaluate black box function f. Traditional settings for this problem assume just the availability of this single function. However, in many cases, cheap approximations to f may be obtainable. For example, the expensive real world behaviour of a robot can be approximated by a cheap computer simulation. We can use these approximations to eliminate low function value regions cheaply and use the expensive evaluations of f in a small but promising region and speedily identify the optimum. We formalise this task as a multi-fidelity bandit problem where the target function and its approximations are sampled from a Gaussian process. We develop MF-GP-UCB, a novel method based on upper confidence bound techniques. In our theoretical analysis we demonstrate that it exhibits precisely the above behaviour and achieves better bounds on the regret than strategies which ignore multi-fidelity information. Empirically, MF-GP-UCB outperforms such naive strategies and other multi-fidelity methods on several synthetic and real experiments.

scholarly journals Variable Selection and Parameter Tuning for BART Modeling in the Fragile Families Challenge

2019 ◽  
Vol 5 ◽  
pp. 237802311982588 ◽  
Author(s):  
Nicole Bohme Carnegie ◽  
James Wu
Keyword(s):  
Variable Selection ◽  
Missing Values ◽  
Linear Models ◽  
Parameter Tuning ◽  
Black Box ◽  
Machine Learning Algorithms ◽  
Outcome Variable ◽  
Fragile Families ◽  
Great Flexibility ◽  
Additive Regression

Our goal for the Fragile Families Challenge was to develop a hands-off approach that could be applied in many settings to identify relationships that theory-based models might miss. Data processing was our first and most time-consuming task, particularly handling missing values. Our second task was to reduce the number of variables for modeling, and we compared several techniques for variable selection: least absolute selection and shrinkage operator, regression with a horseshoe prior, Bayesian generalized linear models, and Bayesian additive regression trees (BART). We found minimal differences in final performance based on the choice of variable selection method. We proceeded with BART for modeling because it requires minimal assumptions and permits great flexibility in fitting surfaces and based on previous success using BART in black-box modeling competitions. In addition, BART allows for probabilistic statements about the predictions and other inferences, which is an advantage over most machine learning algorithms. A drawback to BART, however, is that it is often difficult to identify or characterize individual predictors that have strong influences on the outcome variable.

scholarly journals Computer Adaptive Testing Using Upper-Confidence Bound Algorithm for Formative Assessment

2019 ◽  
Vol 9 (20) ◽  
pp. 4303 ◽  
Author(s):  
Jaroslav Melesko ◽  
Vitalij Novickij
Keyword(s):  
Formative Assessment ◽  
Latent Trait ◽  
Corrective Feedback ◽  
Strong Support ◽  
Adaptive Testing ◽  
Computer Adaptive Testing ◽  
Confidence Bound ◽  
Question Item ◽  
E Learning ◽  
Upper Confidence Bound

There is strong support for formative assessment inclusion in learning processes, with the main emphasis on corrective feedback for students. However, traditional testing and Computer Adaptive Testing can be problematic to implement in the classroom. Paper based tests are logistically inconvenient and are hard to personalize, and thus must be longer to accurately assess every student in the classroom. Computer Adaptive Testing can mitigate these problems by making use of Multi-Dimensional Item Response Theory at cost of introducing several new problems, most problematic of which are the greater test creation complexity, because of the necessity of question pool calibration, and the debatable premise that different questions measure one common latent trait. In this paper a new approach of modelling formative assessment as a Multi-Armed bandit problem is proposed and solved using Upper-Confidence Bound algorithm. The method in combination with e-learning paradigm has the potential to mitigate such problems as question item calibration and lengthy tests, while providing accurate formative assessment feedback for students. A number of simulation and empirical data experiments (with 104 students) are carried out to explore and measure the potential of this application with positive results.

scholarly journals Multi-fidelity black-box optimization for time-optimal quadrotor maneuvers

2021 ◽  
pp. 027836492110333
Author(s):  
Gilhyun Ryou ◽  
Ezra Tal ◽  
Sertac Karaman
Keyword(s):  
Real World ◽  
High Speed ◽  
Analytical Approximation ◽  
Black Box ◽  
Bayesian Optimization ◽  
Optimization Framework ◽  
Quadrotor Aircraft ◽  
Time Optimal ◽  
Feasibility Constraints ◽  
Generation Problem

We consider the problem of generating a time-optimal quadrotor trajectory for highly maneuverable vehicles, such as quadrotor aircraft. The problem is challenging because the optimal trajectory is located on the boundary of the set of dynamically feasible trajectories. This boundary is hard to model as it involves limitations of the entire system, including complex aerodynamic and electromechanical phenomena, in agile high-speed flight. In this work, we propose a multi-fidelity Bayesian optimization framework that models the feasibility constraints based on analytical approximation, numerical simulation, and real-world flight experiments. By combining evaluations at different fidelities, trajectory time is optimized while the number of costly flight experiments is kept to a minimum. The algorithm is thoroughly evaluated for the trajectory generation problem in two different scenarios: (1) connecting predetermined waypoints; (2) planning in obstacle-rich environments. For each scenario, we conduct both simulation and real-world flight experiments at speeds up to 11 m/s. Resulting trajectories were found to be significantly faster than those obtained through minimum-snap trajectory planning.

Identification of Top-K Influencers Based on Upper Confidence Bound and Local Structure

2021 ◽  
pp. 100208
Author(s):  
Mohammed Alshahrani ◽  
Fuxi Zhu ◽  
Soufiana Mekouar ◽  
Mohammed Yahya Alghamdi ◽  
Shichao Liu
Keyword(s):  
Local Structure ◽  
Confidence Bound ◽  
Upper Confidence Bound

scholarly journals Computing Accurate Probabilistic Estimates of One-D Entropy from Equiprobable Random Samples

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 740
Author(s):  
Hoshin V. Gupta ◽  
Mohammad Reza Ehsani ◽  
Tirthankar Roy ◽  
Maria A. Sans-Fuentes ◽  
Uwe Ehret ◽  
...  
Keyword(s):  
Sample Size ◽  
Parameter Tuning ◽  
Gaussian Mixture ◽  
Optimal Number ◽  
Small Sample ◽  
Random Samples ◽  
Data Points ◽  
Probability Mass ◽  
Entropy Estimate ◽  
Log Normal

We develop a simple Quantile Spacing (QS) method for accurate probabilistic estimation of one-dimensional entropy from equiprobable random samples, and compare it with the popular Bin-Counting (BC) and Kernel Density (KD) methods. In contrast to BC, which uses equal-width bins with varying probability mass, the QS method uses estimates of the quantiles that divide the support of the data generating probability density function (pdf) into equal-probability-mass intervals. And, whereas BC and KD each require optimal tuning of a hyper-parameter whose value varies with sample size and shape of the pdf, QS only requires specification of the number of quantiles to be used. Results indicate, for the class of distributions tested, that the optimal number of quantiles is a fixed fraction of the sample size (empirically determined to be ~0.25–0.35), and that this value is relatively insensitive to distributional form or sample size. This provides a clear advantage over BC and KD since hyper-parameter tuning is not required. Further, unlike KD, there is no need to select an appropriate kernel-type, and so QS is applicable to pdfs of arbitrary shape, including those with discontinuous slope and/or magnitude. Bootstrapping is used to approximate the sampling variability distribution of the resulting entropy estimate, and is shown to accurately reflect the true uncertainty. For the four distributional forms studied (Gaussian, Log-Normal, Exponential and Bimodal Gaussian Mixture), expected estimation bias is less than 1% and uncertainty is low even for samples of as few as 100 data points; in contrast, for KD the small sample bias can be as large as -10% and for BC as large as -50%. We speculate that estimating quantile locations, rather than bin-probabilities, results in more efficient use of the information in the data to approximate the underlying shape of an unknown data generating pdf.

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