scholarly journals Bayesian optimization with partially specified queries

2022 ◽  
Author(s):  
Shogo Hayashi ◽  
Junya Honda ◽  
Hisashi Kashima
Keyword(s):  
Black Box ◽  
Bayesian Optimization ◽  
Unknown Input ◽  
Bandit Problem ◽  
Test Functions ◽  
Significant Cost ◽  
Posterior Sampling ◽  
Regret Bounds ◽  
Input Variables ◽  
Real World Datasets

AbstractBayesian optimization (BO) is an approach to optimizing an expensive-to-evaluate black-box function and sequentially determines the values of input variables to evaluate the function. However, it is expensive and in some cases becomes difficult to specify values for all input variables, for example, in outsourcing scenarios where production of input queries with many input variables involves significant cost. In this paper, we propose a novel Gaussian process bandit problem, BO with partially specified queries (BOPSQ). In BOPSQ, unlike the standard BO setting, a learner specifies only the values of some input variables, and the values of the unspecified input variables are randomly determined according to a known or unknown distribution. We propose two algorithms based on posterior sampling for cases of known and unknown input distributions. We further derive their regret bounds that are sublinear for popular kernels. We demonstrate the effectiveness of the proposed algorithms using test functions and real-world datasets.

scholarly journals Optimal Exploitation of Clustering and History Information in Multi-armed Bandit

2019 ◽  
Author(s):  
Djallel Bouneffouf ◽  
Srinivasan Parthasarathy ◽  
Horst Samulowitz ◽  
Martin Wistuba
Keyword(s):  
Real World ◽  
Drug Dosage ◽  
Bandit Problem ◽  
Optimal Exploitation ◽  
Clustering Quality ◽  
History Information ◽  
Regret Bounds ◽  
Real World Datasets ◽  
Latency Minimization ◽  
Exploration Phase

We consider the stochastic multi-armed bandit problem and the contextual bandit problem with historical observations and pre-clustered arms. The historical observations can contain any number of instances for each arm, and the pre-clustering information is a fixed clustering of arms provided as part of the input. We develop a variety of algorithms which incorporate this offline information effectively during the online exploration phase and derive their regret bounds. In particular, we develop the META algorithm which effectively hedges between two other algorithms: one which uses both historical observations and clustering, and another which uses only the historical observations. The former outperforms the latter when the clustering quality is good, and vice-versa. Extensive experiments on synthetic and real world datasets on Warafin drug dosage and web server selectionfor latency minimization validate our theoretical insights and demonstrate that META is a robust strategy for optimally exploiting the pre-clustering information.

scholarly journals Explaining inference queries with bayesian optimization

2021 ◽  
Vol 14 (11) ◽  
pp. 2576-2585
Author(s):  
Brandon Lockhart ◽  
Jinglin Peng ◽  
Weiyuan Wu ◽  
Jiannan Wang ◽  
Eugene Wu
Keyword(s):  
Global Optimum ◽  
Black Box ◽  
Training Data ◽  
Bayesian Optimization ◽  
Categorical Variables ◽  
Warm Start ◽  
Query Result ◽  
Real World Datasets ◽  
Data Inference ◽  
Sql Query

Obtaining an explanation for an SQL query result can enrich the analysis experience, reveal data errors, and provide deeper insight into the data. Inference query explanation seeks to explain unexpected aggregate query results on inference data; such queries are challenging to explain because an explanation may need to be derived from the source, training, or inference data in an ML pipeline. In this paper, we model an objective function as a black-box function and propose BOExplain, a novel framework for explaining inference queries using Bayesian optimization (BO). An explanation is a predicate defining the input tuples that should be removed so that the query result of interest is significantly affected. BO --- a technique for finding the global optimum of a black-box function --- is used to find the best predicate. We develop two new techniques (individual contribution encoding and warm start) to handle categorical variables. We perform experiments showing that the predicates found by BOExplain have a higher degree of explanation compared to those found by the state-of-the-art query explanation engines. We also show that BOExplain is effective at deriving explanations for inference queries from source and training data on a variety of real-world datasets. BOExplain is open-sourced as a Python package at https://github.com/sfu-db/BOExplain.

A MO-BAYESIAN OPTIMIZATION APPROACH USING THE WEIGHTED TCHEBYCHEFF METHOD

2021 ◽  
pp. 1-30
Author(s):  
Arpan Biswas ◽  
Claudio Fuentes ◽  
Christopher Hoyle
Keyword(s):  
Process Model ◽  
Low Cost ◽  
Black Box ◽  
Training Data ◽  
Bayesian Optimization ◽  
Optimization Approach ◽  
Objective Functions ◽  
Multi Objective ◽  
Input Variables ◽  
Future Evaluation

Abstract Bayesian optimization (BO) is a low-cost global optimization tool for expensive black-box objective functions, where we learn from prior evaluated designs, update a posterior surrogate Gaussian process model, and select new designs for future evaluation using an acquisition function. This research focuses upon developing a BO model with multiple black-box objective functions. In the standard Multi-Objective optimization (MOO) problem, the weighted Tchebycheff method is efficiently used to find both convex and non-convex Pareto frontiers. This approach requires knowledge of utopia values before we start optimization. However, in the BO framework, since the functions are expensive to evaluate, it is very expensive to obtain the utopia values as a prior knowledge. Therefore, in this paper, we develop a MO-BO framework where we calibrate with multiple linear regression (MLR) models to estimate the utopia value for each objective as a function of design input variables; the models are updated iteratively with sampled training data from the proposed multi-objective BO. This iteratively estimated mean utopia values is used to formulate the weighted Tchebycheff multi-objective acquisition function. The proposed approach is implemented in optimizing thin tube geometries under constant loading of temperature and pressure, with minimizing the risk of creep-fatigue failure and design cost, along with risk-based and manufacturing constraints. Finally, the model accuracy with frequentist, Bayesian and without MLR-based calibration are compared to true Pareto solutions.

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.

Generating New Space-Filling Test Instances for Continuous Black-Box Optimization

2020 ◽  
Vol 28 (3) ◽  
pp. 379-404
Author(s):  
Mario A. Muñoz ◽  
Kate Smith-Miles
Keyword(s):  
Feature Vector ◽  
State Of The Art ◽  
Evolutionary Process ◽  
Black Box ◽  
Two Dimensional ◽  
Entire Space ◽  
Test Functions ◽  
New Space ◽  
Instance Space ◽  
Different Characteristics

This article presents a method to generate diverse and challenging new test instances for continuous black-box optimization. Each instance is represented as a feature vector of exploratory landscape analysis measures. By projecting the features into a two-dimensional instance space, the location of existing test instances can be visualized, and their similarities and differences revealed. New instances are generated through genetic programming which evolves functions with controllable characteristics. Convergence to selected target points in the instance space is used to drive the evolutionary process, such that the new instances span the entire space more comprehensively. We demonstrate the method by generating two-dimensional functions to visualize its success, and ten-dimensional functions to test its scalability. We show that the method can recreate existing test functions when target points are co-located with existing functions, and can generate new functions with entirely different characteristics when target points are located in empty regions of the instance space. Moreover, we test the effectiveness of three state-of-the-art algorithms on the new set of instances. The results demonstrate that the new set is not only more diverse than a well-known benchmark set, but also more challenging for the tested algorithms. Hence, the method opens up a new avenue for developing test instances with controllable characteristics, necessary to expose the strengths and weaknesses of algorithms, and drive algorithm development.

scholarly journals Adaptive Double-Exploration Tradeoff for Outlier Detection

2020 ◽  
Vol 34 (04) ◽  
pp. 6837-6844
Author(s):  
Xiaojin Zhang ◽  
Honglei Zhuang ◽  
Shengyu Zhang ◽  
Yuan Zhou
Keyword(s):  
Confidence Interval ◽  
Outlier Detection ◽  
Real World ◽  
Efficient Algorithm ◽  
Experimental Results ◽  
Sample Complexity ◽  
Bandit Problem ◽  
Real World Datasets ◽  
Synthetic Datasets ◽  
The Individual

We study a variant of the thresholding bandit problem (TBP) in the context of outlier detection, where the objective is to identify the outliers whose rewards are above a threshold. Distinct from the traditional TBP, the threshold is defined as a function of the rewards of all the arms, which is motivated by the criterion for identifying outliers. The learner needs to explore the rewards of the arms as well as the threshold. We refer to this problem as "double exploration for outlier detection". We construct an adaptively updated confidence interval for the threshold, based on the estimated value of the threshold in the previous rounds. Furthermore, by automatically trading off exploring the individual arms and exploring the outlier threshold, we provide an efficient algorithm in terms of the sample complexity. Experimental results on both synthetic datasets and real-world datasets demonstrate the efficiency of our algorithm.

scholarly journals Black-box combinatorial optimization using models with integer-valued minima

2020 ◽  
Author(s):  
Laurens Bliek ◽  
Sicco Verwer ◽  
Mathijs de Weerdt
Keyword(s):  
Optimization Algorithm ◽  
Surrogate Model ◽  
Optimization Problems ◽  
Random Search ◽  
Continuous Optimization ◽  
Optimal Solution ◽  
Black Box ◽  
Combinatorial Problems ◽  
Bayesian Optimization ◽  
Bayesian Optimization Algorithm

Abstract When a black-box optimization objective can only be evaluated with costly or noisy measurements, most standard optimization algorithms are unsuited to find the optimal solution. Specialized algorithms that deal with exactly this situation make use of surrogate models. These models are usually continuous and smooth, which is beneficial for continuous optimization problems, but not necessarily for combinatorial problems. However, by choosing the basis functions of the surrogate model in a certain way, we show that it can be guaranteed that the optimal solution of the surrogate model is integer. This approach outperforms random search, simulated annealing and a Bayesian optimization algorithm on the problem of finding robust routes for a noise-perturbed traveling salesman benchmark problem, with similar performance as another Bayesian optimization algorithm, and outperforms all compared algorithms on a convex binary optimization problem with a large number of variables.

scholarly journals Modelling human active search in optimizing black-box functions

2020 ◽  
Vol 24 (23) ◽  
pp. 17771-17785
Author(s):  
Antonio Candelieri ◽  
Riccardo Perego ◽  
Ilaria Giordani ◽  
Andrea Ponti ◽  
Francesco Archetti
Keyword(s):  
Active Learning ◽  
Bayesian Learning ◽  
Surrogate Models ◽  
Black Box ◽  
Bayesian Optimization ◽  
Learning Approaches ◽  
Function Learning ◽  
The Subject ◽  
Human Function ◽  
Exploration Exploitation

AbstractModelling human function learning has been the subject of intense research in cognitive sciences. The topic is relevant in black-box optimization where information about the objective and/or constraints is not available and must be learned through function evaluations. In this paper, we focus on the relation between the behaviour of humans searching for the maximum and the probabilistic model used in Bayesian optimization. As surrogate models of the unknown function, both Gaussian processes and random forest have been considered: the Bayesian learning paradigm is central in the development of active learning approaches balancing exploration/exploitation in uncertain conditions towards effective generalization in large decision spaces. In this paper, we analyse experimentally how Bayesian optimization compares to humans searching for the maximum of an unknown 2D function. A set of controlled experiments with 60 subjects, using both surrogate models, confirm that Bayesian optimization provides a general model to represent individual patterns of active learning in humans.

scholarly journals Contextual-Bandit Based Personalized Recommendation with Time-Varying User Interests

2020 ◽  
Vol 34 (04) ◽  
pp. 6518-6525
Author(s):  
Xiao Xu ◽  
Fang Dong ◽  
Yanghua Li ◽  
Shaojian He ◽  
Xin Li
Keyword(s):  
Learning Algorithm ◽  
General Setting ◽  
Personalized Recommendation ◽  
Time Varying ◽  
Bandit Problem ◽  
User Interests ◽  
Specific Preference ◽  
Coefficient Vector ◽  
Real World Datasets ◽  
Efficient Learning

A contextual bandit problem is studied in a highly non-stationary environment, which is ubiquitous in various recommender systems due to the time-varying interests of users. Two models with disjoint and hybrid payoffs are considered to characterize the phenomenon that users' preferences towards different items vary differently over time. In the disjoint payoff model, the reward of playing an arm is determined by an arm-specific preference vector, which is piecewise-stationary with asynchronous and distinct changes across different arms. An efficient learning algorithm that is adaptive to abrupt reward changes is proposed and theoretical regret analysis is provided to show that a sublinear scaling of regret in the time length T is achieved. The algorithm is further extended to a more general setting with hybrid payoffs where the reward of playing an arm is determined by both an arm-specific preference vector and a joint coefficient vector shared by all arms. Empirical experiments are conducted on real-world datasets to verify the advantages of the proposed learning algorithms against baseline ones in both settings.

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