mlsanityData to 14 Oct 2026

Asymptotic Universal Alignment: A New Alignment Framework via Test-Time Scaling

arXiv 2601.08777 ↗First posted 13 Jan 2026cs.LG cs.AI cs.CLcited by 0

On the map: LLM reasoning → Reinforcement learning for reasoning

also in 1 more
Abstract (arXiv)

Aligning large language models (LLMs) to serve users with heterogeneous and potentially conflicting preferences is a central challenge for personalized and trustworthy AI. We formalize an ideal notion of universal alignment through test-time scaling: for each prompt, the model produces k≥ 1 candidate responses and a user selects their preferred one. We introduce (k,f(k))-robust alignment, which requires the k-output model to have win rate f(k) against any other single-output model, and asymptotic universal alignment (U-alignment), which requires f(k)→ 1 as k→∞. Our main result characterizes the optimal convergence rate: there exists a family of single-output policies whose k-sample product policies achieve U-alignment at rate f(k)=frackk+1, and no method can achieve a faster rate in general. We show that popular post-training methods, including Nash learning from human feedback (NLHF), can fundamentally underutilize the benefits of test-time scaling. Even though NLHF is optimal for k=1, sampling from the resulting (often deterministic) policy cannot guarantee win rates above tfrac12 except for an arbitrarily small slack. This stems from a lack of output diversity: existing alignment methods can collapse to a single majority-preferred response, making additional samples redundant. In contrast, our approach preserves output diversity and achieves the optimal test-time scaling rate. In particular, we propose a family of symmetric multi-player alignment games and prove that any symmetric Nash equilibrium policy of the (k+1)-player alignment game achieves the optimal (k,frackk+1)-robust alignment. Finally, we provide theoretical convergence guarantees for self-play learning dynamics in these games and extend the framework to opponents that also generate multiple responses.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning. Builds on 32 of its 47 references that are in the map. First posted on arXiv 13 Jan 2026.

Builds on

32 of 47 references.

Closest ancestors · 1

Same direction, newest first

  1. 2025Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?18 Apr

Other references · 31

  1. 2022Training language models to follow instructions with human feedbackcited by 15,971
  2. 2017Deep reinforcement learning from human preferencescited by 3,912
  3. 2022Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedbackcited by 3,720
  4. 2019Introduction to Online Convex Optimizationcited by 803
  5. 2019Online Learning: A Modern Introduction Using Convex Optimizationcited by 417
  6. 2023Understanding the Effects of RLHF on LLM Generalisation and Diversitycited by 396
  7. 2024Self-Play Preference Optimization for Language Model Alignmentcited by 232
  8. 2023Nash Learning from Human Feedbackcited by 224
  9. 2013Optimization, Learning, and Games with Predictable Sequencescited by 188
  10. 2024A Minimaximalist Approach to Reinforcement Learning from Human Feedbackcited by 144
  11. 2018The Limit Points of (Optimistic) Gradient Descent in Min-Max Optimizationcited by 101
  12. 2024Human Alignment of Large Language Models through Online Preference Optimisationcited by 91
19 more
  1. 2024Iterative Nash Policy Optimization: Aligning LLMs with General Preferences via No-Regret Learningcited by 45
  2. 2023Generative Social Choicecited by 43
  3. 2025Rethinking Fine-Tuning when Scaling Test-Time Compute: Limiting Confidence Improves Mathematical Reasoningcited by 29
  4. 2025Statistical Impossibility and Possibility of Aligning LLMs with Human Preferences: From Condorcet Paradox to Nash Equilibriumcited by 23
  5. 2024Magnetic Preference Optimization: Achieving Last-iterate Convergence for Language Model Alignmentcited by 20
  6. 2025Jackpot! Alignment as a Maximal Lotterycited by 17
  7. 2025Extragradient Preference Optimization (EGPO): Beyond Last-Iterate Convergence for Nash Learning from Human Feedbackcited by 16
  8. 2024Fast Last-Iterate Convergence of Learning in Games Requires Forgetful Algorithmscited by 14
  9. 2019Group Fairness in Committee Selectioncited by 10
  10. 2025Fundamental Limits of Game-Theoretic LLM Alignment: Smith Consistency and Preference Matchingcited by 10
  11. 2024COMAL: A Convergent Meta-Algorithm for Aligning LLMs with General Preferencescited by 8
  12. 2019Approximately Stable Committee Selectioncited by 7
  13. 2025Theoretical Tensions in RLHF: Reconciling Empirical Success with Inconsistencies in Social Choice Theorycited by 7
  14. 2025Multiplayer Nash Preference Optimizationcited by 7
  15. 2025Proximal Point Nash Learning from Human Feedbackcited by 5
  16. 2024Six Candidates Suffice to Win a Voter Majoritycited by 3
  17. 2025Multi-Step Alignment as Markov Games: An Optimistic Online Gradient Descent Approach with Convergence Guaranteescited by 3
  18. 2025Metric Distortion for Tournament Voting and Beyondcited by 2
  19. 2025A few good choicescited by 1

Built on by

Not cited yet.

Similar, not cited

Close in wording, no citation either way

  1. 2025Align-Pro: A Principled Approach to Prompt Optimization for LLM Alignment
  2. 2025Beyond RLHF: A Unified Theoretical Framework of Alignment
  3. 2025AdaBoN: Adaptive Best-of-N Alignment
  4. 2024Self-Play with Adversarial Critic: Provable and Scalable Offline Alignment for Language Models
  5. 2024DeAL: Decoding-time Alignment for Large Language Models
  6. 2025DiffPO: Diffusion-styled Preference Optimization for Efficient Inference-Time Alignment of Large Language Models
  7. 2024SAIL: Self-Improving Efficient Online Alignment of Large Language Models
  8. 2024Language Alignment via Nash-learning and Adaptive feedback