Daily Arxiv

This is a page that curates AI-related papers published worldwide.
All content here is summarized using Google Gemini and operated on a non-profit basis.
Copyright for each paper belongs to the authors and their institutions; please make sure to credit the source when sharing.

Preference Elicitation for Multi-objective Combinatorial Optimization with Active Learning and Maximum Likelihood Estimation

Created by
  • Haebom

Author

Marianne Defresne, Jayanta Mandi, Tias Guns

Outline

This paper addresses a real-world combinatorial optimization problem involving multiple conflicting objectives, such as price, product quality, and sustainability. While computationally efficient methods exist for aggregating multiple objectives into a single objective function (e.g., linear combination), predefining the weights of linear combinations is challenging. As an alternative, interactive learning methods that ask users to compare candidate solutions offer promise. The key challenges are to rapidly generate candidates, learn an objective function that leads to high-quality solutions, and minimize user interactions. This paper proposes a method based on the Constructive Preference Elicitation (CPE) framework that improves three attributes: interaction speed, learning performance, and the number of user interactions. To improve interaction speed, we use a (relaxed) solution pool. To enhance learning performance, we employ maximum likelihood estimation of the Bradley-Terry preference model. To reduce the number of user interactions, we employ an ensemble-based acquisition function inspired by active learning. Experiments on PC configuration tasks and realistic multi-instance routing problems demonstrate that our method achieves faster query selection, fewer queries, and higher-quality combinatorial solutions than existing CPE methods.

Takeaways, Limitations

Takeaways:
An efficient interactive learning method for multi-objective combinatorial optimization problems is presented.
Improved interaction speed, learning performance, and number of user interactions in the CPE framework.
Demonstrated superior performance over existing methods in real-world problems (PC configuration, multi-instance routing).
Effective use of the Bradley-Terry model and ensemble-based acquisition functions.
Limitations:
Further research is needed on the generalization performance of the proposed method.
Applicability verification is required for various types of combinatorial optimization problems.
Dependence on the accuracy of the user preference model.
Scalability review for large-scale problems is required.
👍