insikt - Optimization - # Surrogate-Based Optimization

Enhancing Black-Box Optimization with Polynomial Surrogates: PMBO Study

Q: How does the performance of PMBO compare to other state-of-the-art algorithms

PMBO demonstrates competitive performance compared to other state-of-the-art algorithms, such as Bayesian optimization, CMA-ES, and BADs. In benchmarking against these methods on various analytic functions from the BBOB test suite, PMBO consistently showed robustness and efficiency in optimizing the objective function. The results indicated that PMBO outperformed Bayesian optimization with fixed hyperparameters in terms of convergence speed and accuracy. Additionally, when compared to CMA-ES and BADs, PMBO showcased comparable or even superior performance in certain scenarios.

Q: What are the limitations of PMBO in high-dimensional problems

The primary limitation of PMBO lies in its scalability to high-dimensional problems. While it performs well up to dimension m = 5 by efficiently updating the complexity of the polynomial model based on sample size, this approach becomes challenging for higher dimensions due to computational constraints. The number of samples required for accurate least-squares solutions increases significantly with dimensionality, making it impractical for large-scale optimization tasks.

Q: How can hybridization with evolutionary algorithms enhance the performance of PMBO

Hybridization with evolutionary algorithms can enhance the performance of PMBO by leveraging their strengths in exploring complex landscapes with high local variations. By combining the global structure imposed by polynomial regression in PMBO with the exploration capabilities of evolutionary algorithms like CMA-ES or hybrid solutions like BADs, a more robust and efficient optimization strategy can be achieved. This hybrid approach can potentially address limitations faced by individual methods when dealing with specific types of objective functions or problem complexities.

Centrala begrepp

PMBO introduces a novel approach by combining polynomial approximation with Bayesian optimization, outperforming classic methods and showing robustness in low-dimensional optimization problems.

Sammanfattning

PMBO is a surrogate-based black-box optimization method that combines polynomial approximation with Bayesian optimization. The results show its superiority over classic methods and robustness in addressing low-dimensional optimization problems. PMBO offers a unique perspective on the landscape of objective functions through its simple nature of polynomials.

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Statistik

PMBO outperforms classic Bayesian optimization.
PMBO shows robustness in low-dimensional optimization.
PMBO combines polynomial approximation with Bayesian optimization.

Citat

"One can show that interpolation by polynomials in Chebyshev points is equivalent to interpolation of periodic functions by series of sines and cosines in equispaced points." - Prof Lloyd N. Trefethen

Viktiga insikter från

PMBO

by Janina Schre... på arxiv.org 03-13-2024

https://arxiv.org/pdf/2403.07485.pdf

Djupare frågor

How does the performance of PMBO compare to other state-of-the-art algorithms

PMBO demonstrates competitive performance compared to other state-of-the-art algorithms, such as Bayesian optimization, CMA-ES, and BADs. In benchmarking against these methods on various analytic functions from the BBOB test suite, PMBO consistently showed robustness and efficiency in optimizing the objective function. The results indicated that PMBO outperformed Bayesian optimization with fixed hyperparameters in terms of convergence speed and accuracy. Additionally, when compared to CMA-ES and BADs, PMBO showcased comparable or even superior performance in certain scenarios.

What are the limitations of PMBO in high-dimensional problems

The primary limitation of PMBO lies in its scalability to high-dimensional problems. While it performs well up to dimension m = 5 by efficiently updating the complexity of the polynomial model based on sample size, this approach becomes challenging for higher dimensions due to computational constraints. The number of samples required for accurate least-squares solutions increases significantly with dimensionality, making it impractical for large-scale optimization tasks.

How can hybridization with evolutionary algorithms enhance the performance of PMBO

Hybridization with evolutionary algorithms can enhance the performance of PMBO by leveraging their strengths in exploring complex landscapes with high local variations. By combining the global structure imposed by polynomial regression in PMBO with the exploration capabilities of evolutionary algorithms like CMA-ES or hybrid solutions like BADs, a more robust and efficient optimization strategy can be achieved. This hybrid approach can potentially address limitations faced by individual methods when dealing with specific types of objective functions or problem complexities.