mlsanityData to 14 Oct 2026

On the Convergence of Self-Improving Online LLM Alignment

arXiv 2606.31524 ↗First posted 30 Jun 2026cs.LG cs.AI stat.MLcited by 1

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

also in 1 more
Abstract (arXiv)

The Self-Improving Alignment (SAIL) algorithm addresses distribution shift by reducing a bilevel formulation of the problem to an efficient, single-level method. Empirically, SAIL has demonstrated strong performance on this task. However, a formal analysis of its convergence properties has been lacking. We identify a key theoretical challenge: the standard SAIL objective function is not guaranteed to be strongly concave due to unfavorable properties of its Hessian. To address this limitation, we propose a regularized objective, SAIL-RevKL, which incorporates a reverse Kullback-Leibler (KL) divergence penalty to improve the optimization landscape. Our central theoretical contribution is to prove that this regularized objective satisfies the Polyak-Lojasiewicz (PL) condition within a bounded parameter space. We establish global convergence guarantees, achieving a near-linear sample complexity. We further validate the effectiveness and stability of SAIL-RevKL through empirical evaluations, demonstrating that it outperforms the vanilla SAIL on both MuJoCo benchmarks and LLM alignment tasks.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Placed in LLM preference optimization methods, one of 10 directions in LLM alignment / RLHF / preference optimisation. Builds on 33 of its 47 references that are in the map. First posted on arXiv 30 Jun 2026.

Builds on

33 of 47 references.

Closest ancestors · 2

Same direction, newest first

  1. 2024SAIL: Self-Improving Efficient Online Alignment of Large Language Models21 Jun
  2. 2023A General Theoretical Paradigm to Understand Learning from Human Preferences18 Oct

Other references · 31

  1. 2023GPT-4 Technical Reportcited by 18,396
  2. 2023Judging LLM-as-a-Judge with MT-Bench and Chatbot Arenacited by 8,626
  3. 2023Direct Preference Optimization: Your Language Model is Secretly a Reward Modelcited by 8,065
  4. 2021Convex optimizationcited by 2,515
  5. 2019Fine-Tuning Language Models from Human Preferencescited by 2,150
  6. 2019Meta-World: A Benchmark and Evaluation for Multi-Task and Meta Reinforcement Learningcited by 1,204
  7. 2018DeepMind Control Suitecited by 956
  8. 2022Fine-Tuning can Distort Pretrained Features and Underperform Out-of-Distributioncited by 739
  9. 2023UltraFeedback: Boosting Language Models with Scaled AI Feedbackcited by 406
  10. 2023SLiC-HF: Sequence Likelihood Calibration with Human Feedbackcited by 401
  11. 2022Last Layer Re-Training is Sufficient for Robustness to Spurious Correlationscited by 381
  12. 2021PEBBLE: Feedback-Efficient Interactive Reinforcement Learning via Relabeling Experience and Unsupervised Pre-trainingcited by 302
19 more
  1. 2024PKU-SafeRLHF: Towards Multi-Level Safety Alignment for LLMs with Human Preferencecited by 261
  2. 2023Principled Reinforcement Learning with Human Feedback from Pairwise or K-wise Comparisonscited by 247
  3. 2018Stochastic Variance-Reduced Policy Gradientcited by 106
  4. 2019Sample Complexity of Reinforcement Learning using Linearly Combined Model Ensemblescited by 100
  5. 2022SURF: Semi-supervised Reward Learning with Data Augmentation for Feedback-efficient Preference-based Reinforcement Learningcited by 97
  6. 2022An Improved Analysis of (Variance-Reduced) Policy Gradient and Natural Policy Gradient Methodscited by 68
  7. 2019Sample Efficient Policy Gradient Methods with Recursive Variance Reductioncited by 60
  8. 2019An Improved Convergence Analysis of Stochastic Variance-Reduced Policy Gradientcited by 59
  9. 2023Towards Last-layer Retraining for Group Robustness with Fewer Annotationscited by 54
  10. 2023On Penalty Methods for Nonconvex Bilevel Optimization and First-Order Stochastic Approximationcited by 51
  11. 2024Principled Penalty-based Methods for Bilevel Reinforcement Learning and RLHFcited by 41
  12. 2023PARL: A Unified Framework for Policy Alignment in Reinforcement Learning from Human Feedbackcited by 40
  13. 2023On Finding Small Hyper-Gradients in Bilevel Optimization: Hardness Results and Improved Analysiscited by 39
  14. 2024A Critical Evaluation of AI Feedback for Aligning Large Language Modelscited by 36
  15. 2024Reward Model Learning vs. Direct Policy Optimization: A Comparative Analysis of Learning from Human Preferencescited by 27
  16. 2024A Sharper Global Convergence Analysis for Average Reward Reinforcement Learning via an Actor-Critic Approachcited by 15
  17. 2024Sample-Efficient Constrained Reinforcement Learning with General Parameterizationcited by 11
  18. 2024Bilevel reinforcement learning via the development of hyper-gradient without lower-level convexitycited by 10
  19. 2025On The Sample Complexity Bounds In Bilevel Reinforcement Learningcited by 10

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Non-Expansive Two-Time-Scale Stochastic Approximation: A Fixed-Schedule One-Quarter Barrier and Bias-Corrected Accelerationcited by 0

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