Back to Blackwell: Closing the Loop on Intransitivity in Multi-Objective Preference Fine-Tuning

2026-02-21

AI Summary

This work addresses the challenge of intransitive (cyclic) preferences in multi-objective preference tuning, which undermines the assumption of a globally optimal policy inherent in conventional approaches. The study presents the first extension of Blackwell optimality to multi-objective settings with intransitive preferences, introducing a game-theoretic solution concept termed Maximum-Entropy Blackwell Winner (MaxEntBW). Building on this foundation, the authors propose PROSPER, an efficient, scalarization-free preference tuning algorithm that integrates an LLM-as-a-Judge feedback mechanism. Empirical evaluations demonstrate that PROSPER significantly outperforms existing baselines on both instruction-following and general dialogue benchmarks. To further validate its effectiveness and scalability, the authors release open-source models with 3B and 7B parameters.

Technology Category

• Humans and AI: Learning Human Values and Preferences
• Machine Learning: Learning Preferences or Rankings
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

A recurring challenge in preference fine-tuning (PFT) is handling $\textit{intransitive}$ (i.e., cyclic) preferences. Intransitive preferences often stem from either $\textit{(i)}$ inconsistent rankings along a single objective or $\textit{(ii)}$ scalarizing multiple objectives into a single metric. Regardless of their source, the downstream implication of intransitive preferences is the same: there is no well-defined optimal policy, breaking a core assumption of the standard PFT pipeline. In response, we propose a novel, game-theoretic solution concept -- the $\textit{Maximum Entropy Blackwell Winner}$ ($\textit{MaxEntBW}$) -- that is well-defined under multi-objective intransitive preferences. To enable computing MaxEntBWs at scale, we derive $\texttt{PROSPER}$: a provably efficient PFT algorithm. Unlike prior self-play techniques, $\texttt{PROSPER}$ directly handles multiple objectives without requiring scalarization. We then apply $\texttt{PROSPER}$ to the problem of fine-tuning large language models (LLMs) from multi-objective LLM-as-a-Judge feedback (e.g., rubric-based judges), a setting where both sources of intransitivity arise. We find that $\texttt{PROSPER}$ outperforms all baselines considered across both instruction following and general chat benchmarks, releasing trained model checkpoints at the 7B and 3B parameter scales.

Problem

• intransitive preferences
• multi-objective preference fine-tuning
• preference fine-tuning
• cyclic preferences
• optimal policy

Innovation

• intransitive preferences
• multi-objective preference fine-tuning
• Maximum Entropy Blackwell Winner
• PROSPER
• LLM-as-a-Judge