Impact of Training Instance Selection on Automated Algorithm Selection Models for Numerical Black-box Optimization

Core Concepts

The choice of training instances significantly impacts the performance of automated algorithm selection models for numerical black-box optimization problems.

Abstract

The authors investigate the impact of training instance selection on automated algorithm selection (AAS) models for numerical black-box optimization problems. They use the recently proposed MA-BBOB function generator to create a large set of 11,800 functions in 2D and 5D dimensions. The authors first analyze the complementarity of the generated functions and the original BBOB functions in terms of problem properties and algorithm performance. They find that the generated functions complement the BBOB set by filling unoccupied regions of the feature space, but the performance complementarity within their portfolio of 8 algorithms is limited. The authors then evaluate three training instance selection methods - random sampling, greedy diversity-based selection, and using the original BBOB functions. They train XGBoost classification models on these training sets and evaluate their performance on various test sets. The results show that the distribution of the training set relative to the test set is a crucial factor. Models trained on randomly sampled instances perform best on unseen test data, while models trained on greedily selected instances perform better on test sets with a similar distribution. Using the BBOB functions alone for training leads to poor generalization. Increasing the training set size can help mitigate the negative effects of non-matching training and test distributions. The authors conclude that the choice of training instances is an important consideration for developing robust and generalizable AAS models, especially when the distribution of practical optimization problems is unknown.

Stats

The authors generated 11,800 functions in 2D and 5D dimensions using the MA-BBOB function generator. They collected performance data for 8 optimization algorithms on these 11,800 functions, with 15 independent runs per function (50 runs for the BBOB functions).

Quotes

"The choice of training instances significantly impacts the performance of automated algorithm selection models for numerical black-box optimization problems." "Models trained on randomly sampled instances perform best on unseen test data, while models trained on greedily selected instances perform better on test sets with a similar distribution." "Increasing the training set size can help mitigate the negative effects of non-matching training and test distributions."

Key Insights Distilled From

Impact of Training Instance Selection on Automated Algorithm Selection Models for Numerical Black-box Optimization

by Konstantin D... at arxiv.org 04-12-2024

https://arxiv.org/pdf/2404.07539.pdf

Deeper Inquiries

How can we efficiently sample training instances when the distribution of practical optimization problems is unknown

Efficiently sampling training instances when the distribution of practical optimization problems is unknown can be challenging but crucial for the generalization of Automated Algorithm Selection (AAS) models. One approach is to use a diverse set of instances that cover a wide range of problem characteristics. This can be achieved by incorporating instances that represent different problem complexities, structures, and features. One method is to use clustering techniques to group instances based on their similarities and differences. By selecting instances from different clusters, we can ensure a diverse representation of the problem space. Additionally, active learning strategies can be employed to iteratively select instances that provide the most information gain, helping to improve the model's generalization ability. Another approach is to incorporate domain knowledge or expert input to guide the selection of training instances. Experts can provide insights into the types of problems that are commonly encountered in practice, helping to tailor the training set to be more representative of real-world scenarios. Furthermore, techniques such as transfer learning can be utilized to leverage knowledge from related domains or previously seen instances to improve the generalization of the AAS model. By transferring information from known instances to new, unseen instances, the model can adapt more effectively to different problem distributions.

What other instance selection methods beyond random and greedy diversity-based sampling could be explored to improve the generalization of AAS models

Beyond random and greedy diversity-based sampling, several other instance selection methods can be explored to enhance the generalization of AAS models: Algorithm Performance-Based Selection: Instances can be selected based on the historical performance of algorithms on similar problems. By considering the strengths and weaknesses of algorithms on specific problem characteristics, the training set can be tailored to improve the model's predictive accuracy. Hybrid Sampling Strategies: Combining multiple sampling techniques, such as random, diversity-based, and performance-based sampling, can provide a more comprehensive representation of the problem space. Hybrid strategies can leverage the benefits of each method to create a more robust training set. Active Learning: Incorporating active learning techniques allows the model to interactively select instances that are most informative for improving its performance. By focusing on instances that are most uncertain or challenging, the model can adapt and learn more effectively. Meta-Learning: Utilizing meta-learning approaches, where the model learns how to learn from different instances, can enhance the generalization ability of AAS models. By capturing patterns and relationships across instances, meta-learning can improve the model's adaptability to new problem distributions.

How can the insights from this study on numerical black-box optimization be extended to other domains where automated algorithm selection is applied, such as combinatorial optimization or machine learning hyperparameter tuning

The insights from this study on numerical black-box optimization can be extended to other domains where automated algorithm selection is applied, such as combinatorial optimization or machine learning hyperparameter tuning, in the following ways: Feature Engineering: Similar to numerical black-box optimization, feature engineering plays a crucial role in algorithm selection for combinatorial optimization and hyperparameter tuning. By identifying relevant features that capture the characteristics of the problem instances, AAS models can make more informed decisions. Instance Representation: The concept of generating diverse problem instances, as explored in numerical black-box optimization, can be applied to combinatorial optimization and hyperparameter tuning. By creating a varied set of instances that cover different problem structures and complexities, AAS models can better generalize to unseen scenarios. Transfer Learning: The use of transfer learning techniques, inspired by the study on numerical black-box optimization, can be beneficial in combinatorial optimization and hyperparameter tuning. By transferring knowledge from known instances to new problem domains, AAS models can adapt more efficiently and improve their performance on diverse problem sets. Domain-Specific Adaptations: Tailoring the insights and methodologies from numerical black-box optimization to the specific characteristics of combinatorial optimization and hyperparameter tuning can enhance the effectiveness of AAS models in these domains. By considering the unique challenges and requirements of each domain, AAS models can be optimized for better performance and generalization.