Geometric Preference Elicitation for Minimax Regret Optimization in Uncertainty Matroids

2025-03-24

AI Summary

This paper addresses matroid optimization under weight uncertainty, where only the feasible weight domain is known and no explicit preference information is available. Method: We propose a geometric preference elicitation framework that iteratively refines the parameter uncertainty region via pairwise comparisons of preferences induced by matroid base structures—bypassing linear programming solvers and explicit minimax regret computation in each iteration. The approach tightly integrates structured preference queries with intrinsic geometric properties of matroids, including base polytopes and face structures. Contribution/Results: To our knowledge, this is the first method to unify matroid structure with geometric preference elicitation. Experiments across four canonical matroid classes demonstrate substantial reductions in query complexity and faster convergence, outperforming state-of-the-art preference elicitation methods in efficiency while guaranteeing approximation to the minimax regret optimal solution.

Technology Category

• Knowledge Representation and Reasoning: Preferences
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Learning Preferences or Rankings

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

This paper presents an efficient preference elicitation framework for uncertain matroid optimization, where precise weight information is unavailable, but insights into possible weight values are accessible. The core innovation of our approach lies in its ability to systematically elicit user preferences, aligning the optimization process more closely with decision-makers' objectives. By incrementally querying preferences between pairs of elements, we iteratively refine the parametric uncertainty regions, leveraging the structural properties of matroids. Our method aims to achieve the exact optimum by reducing regret with a few elicitation rounds. Additionally, our approach avoids the computation of Minimax Regret and the use of Linear programming solvers at every iteration, unlike previous methods. Experimental results on four standard matroids demonstrate that our method reaches optimality more quickly and with fewer preference queries than existing techniques.

Problem

• Elicit user preferences for uncertain matroid optimization
• Reduce regret with minimal preference queries
• Avoid Minimax Regret computation in each iteration

Innovation

• Elicits user preferences via pairwise element queries
• Refines uncertainty regions using matroid properties
• Avoids Minimax Regret computation per iteration