Escaping the KL Agreement Trap in On-Policy Distillation

Haoran Xin; Anhao Zhao; Ying Sun; Jin Li; Xiaoyu Shen; Hui Xiong

Escaping the KL Agreement Trap in On-Policy Distillation

Haoran Xin, Anhao Zhao, Ying Sun, Jin Li, Xiaoyu Shen, Hui Xiong

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Abstract

On-policy distillation (OPD) provides dense token-level supervision by asking a teacher to score student-generated rollouts. However, when the student drifts into an unrecoverable prefix, the teacher may locally agree with the degraded state, producing low reverse KL but little corrective training signal. We identify this persistent regime as a low-KL agreement trap. Further analyses show that tokens during and after such traps produce less useful supervision signals. We propose KAT (KL Agreement Trap Termination), an online OPD termination rule that detects persistent low-KL agreement with a dynamic training-adaptive threshold. By filtering weak supervision from degenerate agreement, KAT improves avg@k accuracy by 2.66% and pass@k by 3.43% across four mathematical benchmarks, while reducing average rollout length by 59.73%.

Anthology ID:: 2026.emnlp-main.1817
Volume:: Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
Month:: October
Year:: 2026
Address:: Budapest, Hungary
Editors:: Hung-Yi Lee, Sunipa Dev, Jessy Li, Desmond Elliott
Venue:: EMNLP
SIG:: SIGDAT
Publisher:: Association for Computational Linguistics
Note:
Pages:: 41418–41431
Language:
URL:: https://aclanthology.org/2026.emnlp-main.1817/
DOI:
Bibkey:
Cite (ACL):: Haoran Xin, Anhao Zhao, Ying Sun, Jin Li, Xiaoyu Shen, and Hui Xiong. 2026. Escaping the KL Agreement Trap in On-Policy Distillation. In Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing, pages 41418–41431, Budapest, Hungary. Association for Computational Linguistics.
Cite (Informal):: Escaping the KL Agreement Trap in On-Policy Distillation (Xin et al., EMNLP 2026)
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PDF:: https://aclanthology.org/2026.emnlp-main.1817.pdf

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@inproceedings{xin-etal-2026-escaping,
    title = "Escaping the {KL} Agreement Trap in On-Policy Distillation",
    author = "Xin, Haoran  and
      Zhao, Anhao  and
      Sun, Ying  and
      Li, Jin  and
      Shen, Xiaoyu  and
      Xiong, Hui",
    editor = "Lee, Hung-Yi  and
      Dev, Sunipa  and
      Li, Jessy  and
      Elliott, Desmond",
    booktitle = "Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing",
    month = oct,
    year = "2026",
    address = "Budapest, Hungary",
    publisher = "Association for Computational Linguistics",
    url = "https://aclanthology.org/2026.emnlp-main.1817/",
    pages = "41418--41431",
    ISBN = "979-8-89176-459-0",
    abstract = "On-policy distillation (OPD) provides dense token-level supervision by asking a teacher to score student-generated rollouts. However, when the student drifts into an unrecoverable prefix, the teacher may locally agree with the degraded state, producing low reverse KL but little corrective training signal. We identify this persistent regime as a low-KL agreement trap. Further analyses show that tokens during and after such traps produce less useful supervision signals. We propose KAT (KL Agreement Trap Termination), an online OPD termination rule that detects persistent low-KL agreement with a dynamic training-adaptive threshold. By filtering weak supervision from degenerate agreement, KAT improves avg@k accuracy by 2.66{\%} and pass@k by 3.43{\%} across four mathematical benchmarks, while reducing average rollout length by 59.73{\%}."
}

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%0 Conference Proceedings
%T Escaping the KL Agreement Trap in On-Policy Distillation
%A Xin, Haoran
%A Zhao, Anhao
%A Sun, Ying
%A Li, Jin
%A Shen, Xiaoyu
%A Xiong, Hui
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-459-0
%F xin-etal-2026-escaping
%X On-policy distillation (OPD) provides dense token-level supervision by asking a teacher to score student-generated rollouts. However, when the student drifts into an unrecoverable prefix, the teacher may locally agree with the degraded state, producing low reverse KL but little corrective training signal. We identify this persistent regime as a low-KL agreement trap. Further analyses show that tokens during and after such traps produce less useful supervision signals. We propose KAT (KL Agreement Trap Termination), an online OPD termination rule that detects persistent low-KL agreement with a dynamic training-adaptive threshold. By filtering weak supervision from degenerate agreement, KAT improves avg@k accuracy by 2.66% and pass@k by 3.43% across four mathematical benchmarks, while reducing average rollout length by 59.73%.
%U https://aclanthology.org/2026.emnlp-main.1817/
%P 41418-41431

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Markdown (Informal)

[Escaping the KL Agreement Trap in On-Policy Distillation](https://aclanthology.org/2026.emnlp-main.1817/) (Xin et al., EMNLP 2026)

Escaping the KL Agreement Trap in On-Policy Distillation (Xin et al., EMNLP 2026)

ACL

Haoran Xin, Anhao Zhao, Ying Sun, Jin Li, Xiaoyu Shen, and Hui Xiong. 2026. Escaping the KL Agreement Trap in On-Policy Distillation. In Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing, pages 41418–41431, Budapest, Hungary. Association for Computational Linguistics.