mlsanityData to 14 Oct 2026

When Are Two RLHF Objectives the Same?

arXiv 2509.11298 ↗First posted 14 Sep 2025cs.LG cs.AI cs.CLcited by 0

On the map: LLM alignment / RLHF / preference optimisation → LLM preference optimization methods

Abstract (arXiv)

The preference optimization literature contains many proposed objectives, often presented as distinct improvements. We introduce Opal, a canonicalization algorithm that determines whether two preference objectives are algebraically equivalent by producing either a canonical form or a concrete witness of non-equivalence. Applying Opal reveals that many widely used methods optimize the same underlying objective, while others are provably distinct. For example, batch normalization can cause the same response pair to receive different gradients depending on batch composition. We identify a small set of structural mechanisms that give rise to genuinely different objectives; most remaining differences are reparameterizations.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in LLM preference optimization methods, one of 10 directions in LLM alignment / RLHF / preference optimisation. Builds on 18 of its 36 references that are in the map. First posted on arXiv 14 Sep 2025.

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18 of 36 references.

Closest ancestors · 8

Same direction, newest first

  1. 2025A Survey of Direct Preference Optimization12 Mar
  2. 2025Reward-aware Preference Optimization: A Unified Mathematical Framework for Model Alignment31 Jan
  3. 2024RainbowPO: A Unified Framework for Combining Improvements in Preference Optimization5 Oct
  4. 2024SimPO: Simple Preference Optimization with a Reference-Free Reward23 May
  5. 2024ORPO: Monolithic Preference Optimization without Reference Model12 Mar
  6. 2024Generalized Preference Optimization: A Unified Approach to Offline Alignment8 Feb
  7. 2023A General Theoretical Paradigm to Understand Learning from Human Preferences18 Oct
  8. 2022Training language models to follow instructions with human feedback4 Mar

Other references · 10

  1. 2017Proximal Policy Optimization Algorithmscited by 15,215
  2. 2024DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Modelscited by 9,379
  3. 2023Direct Preference Optimization: Your Language Model is Secretly a Reward Modelcited by 8,065
  4. 2017Deep reinforcement learning from human preferencescited by 3,912
  5. 2023SLiC-HF: Sequence Likelihood Calibration with Human Feedbackcited by 401
  6. 2019Gradient Descent Maximizes the Margin of Homogeneous Neural Networkscited by 320
  7. 2024Self-Play Preference Optimization for Language Model Alignmentcited by 232
  8. 2023Nash Learning from Human Feedbackcited by 224
  9. 2020Directional convergence and alignment in deep learningcited by 178
  10. 2024DPO Meets PPO: Reinforced Token Optimization for RLHFcited by 127

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  1. 2024Controllable Preference Optimization: Toward Controllable Multi-Objective Alignment
  2. 2024REFA: Reference Free Alignment for multi-preference optimization
  3. 2025Multi-Objective Preference Optimization: Improving Human Alignment of Generative Models
  4. 2025REWARD CONSISTENCY: Improving Multi-Objective Alignment from a Data-Centric Perspective
  5. 2026Conditional Equivalence of DPO and RLHF: Implicit Assumption, Failure Modes, and Provable Alignment
  6. 2025Beyond RLHF: A Unified Theoretical Framework of Alignment
  7. 2026Preference Tuning as Spectral Update Reorganization
  8. 2025Self-Improvement Towards Pareto Optimality: Mitigating Preference Conflicts in Multi-Objective Alignment