MoPLEx: Estimating Plackett-Luce Mixture Models for Multi-Objective Alignment

• URL: http://arxiv.org/abs/2608.25200v2
• Date: Sun, 30 Aug 2026 15:16:22 GMT
• Title: MoPLEx: Estimating Plackett-Luce Mixture Models for Multi-Objective Alignment
• Abstract summary: We study learning a mixture of $k$ Plackett-Luce models from multi-way ranking responses from annotators.<n>We design an efficient algorithm to address this issue by first augmenting the rankings to a larger size.<n>We find that the gradient-based approximation estimates true probabilities with less than 5% error on models with up to 34 billion parameters.
• Score: 21.741170599896307
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study learning a mixture of $k$ Plackett-Luce models from multi-way ranking responses from annotators that may represent heterogeneous underlying preferences. This problem has many applications in AI alignment and preference optimization. Prior work has studied mixtures of Bradley-Terry models from pairwise comparisons. However, estimating a mixture of multi-way ranking models can become theoretically unidentifiable when $k$ exceeds $m/2$, where $m$ is the ranking length. We design an efficient algorithm to address this issue by first augmenting the rankings to a larger size (e.g., generating comparisons from a base model), followed by a gradient-based estimation to reduce inference cost (in the input embedding space). With this procedure in mind, we then fit a mixture of Plackett-Luce (PL) models via an expectation-maximization-style iteration, or MoPLEx in short. We conduct extensive experiments to verify this algorithm. First, we find that the gradient-based approximation estimates true probabilities with less than 5% error on models with up to 34 billion parameters. Second, MoPLEx improves clustering and ranking accuracy by an average of 43.7% and 15.2% over baselines using a single PL model or a mixture of Bradley-Terry models, on UltraFeedback and PERSONA datasets. These results demonstrate the effectiveness of MoPLEx for tackling multi-way rankings following heterogeneous preferences through measuring alignment via gradients.

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