arxiv_ml 85% Match Research Paper Machine learning engineers,Optimization researchers,Robotics engineers,Data scientists 20 hours ago

Bayesian Optimization by Kernel Regression and Density-based Exploration

reinforcement-learning › robotics-rl

📄 Abstract

Abstract: Bayesian optimization is highly effective for optimizing expensive-to-evaluate black-box functions, but it faces significant computational challenges due to the high computational complexity of Gaussian processes, which results in a total time complexity that is quartic with respect to the number of iterations. To address this limitation, we propose the Bayesian Optimization by Kernel regression and density-based Exploration (BOKE) algorithm. BOKE uses kernel regression for efficient function approximation, kernel density for exploration, and integrates them into the confidence bound criteria to guide the optimization process, thus reducing computational costs to quadratic. Our theoretical analysis rigorously establishes the global convergence of BOKE and ensures its robustness in noisy settings. Through extensive numerical experiments on both synthetic and real-world optimization tasks, we demonstrate that BOKE not only performs competitively compared to Gaussian process-based methods and several other baseline methods but also exhibits superior computational efficiency. These results highlight BOKE's effectiveness in resource-constrained environments, providing a practical approach for optimization problems in engineering applications.

Key Contributions

The paper introduces the BOKE algorithm, a novel Bayesian optimization approach that uses kernel regression for efficient function approximation and density-based exploration. By integrating these into the confidence bound criteria, BOKE significantly reduces computational costs from quartic to quadratic complexity compared to Gaussian process-based methods, while rigorously proving global convergence and robustness in noisy settings.

Business Value

Enables faster and more efficient optimization of complex systems and processes where evaluations are costly, such as hyperparameter tuning for ML models, material design, or robotic control.

Paper Metadata

Innovation Type

Algorithmic Innovation

Deployment Feasibility

Feasible for applications where function evaluations are expensive. Requires implementation of the BOKE algorithm.

Limitations Addressed

High computational complexity (quartic) of Gaussian processes in traditional Bayesian optimization, which limits scalability with the number of iterations.

Performance Gains

Reduces total time complexity from quartic to quadratic with respect to the number of iterations compared to Gaussian process-based methods.

Technical Tags

Bayesian optimizationkernel regressiondensity-based explorationblack-box functionscomputational complexityglobal convergencenoisy settingsGaussian processes

Research Topics

OptimizationMachine LearningBayesian MethodsAlgorithm Design

Methods & Architectures

Bayesian Optimization by Kernel regression and density-based Exploration (BOKE)Kernel regressionDensity-based explorationConfidence bound criteria

Applications & Tasks

Hyperparameter Optimization Robotics Engineering Design Scientific Experimentation Optimizing expensive-to-evaluate functionsReducing computational complexity in Bayesian optimizationEnsuring global convergence in noisy environments Efficiently finding the optimum of black-box functionsAccelerating Bayesian optimization processes

Datasets & Benchmarks

Benchmarks

Synthetic optimization tasks • Real-world optimization tasks (performance competitive with GP-based methods)

Computational costGlobal convergenceRobustness in noisy settings

Related Fields

OptimizationMachine LearningStatisticsRoboticsHyperparameter Tuning

Keywords

Bayesian optimizationkernel regressiondensity estimationblack-box optimizationcomputational complexityGaussian processesoptimization algorithmshyperparameter tuning

Academic Context

#Optimization#Machine Learning#Bayesian Methods#Algorithm Design

Commercial Potential

Potential Products

Optimization librariesHyperparameter tuning services

Target Industries

TechnologyManufacturingAutomotiveRoboticsPharmaceuticals

Use Case Examples

Optimizing hyperparameters for deep learning modelsFinding optimal parameters for robotic control policiesDesigning new materials with desired properties

Competitive Edge

Offers a more computationally efficient alternative to traditional Gaussian process-based Bayesian optimization, particularly for problems requiring many iterations, while maintaining theoretical guarantees.

Market Opportunity

Large market for optimization tools and services, especially in ML and engineering.

Revenue Models

Licensing of the BOKE algorithmintegration into commercial optimization software.

Resource Requirements

Compute Needs

Moderate computational resources, significantly less than GP-based methods for large numbers of iterations.

Data Requirements

Data points generated from evaluating the black-box function.

Deployment Constraints

Effectiveness depends on the assumptions of kernel regression and density estimation holding for the target function.

Scalability

Scales quadratically with the number of iterations, a significant improvement over quartic scaling of GP-based methods.

Production Readiness

Maturity Level

Research/Development

Time to Market

Short to medium-term for integration into optimization tools.

Patent Potential

Moderate, related to the BOKE algorithm and its specific components.

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