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Online Difficulty Filtering for Reasoning Oriented Reinforcement Learning

Paper · 2026 · Sanghwan Bae, Jiwoo Hong, Min Young Lee et al.

Summary

Reinforcement learning with verifiable rewards (RLVR) can improve LLM reasoning, but binary rewards are sparse. Prompts that a policy always solves, or never solves, contribute no gradient. This makes the difficulty of training prompts critical. The authors give a theoretical justification for online, difficulty-aware filtering that until now was applied mostly as a heuristic.

They prove that each prompt's reward variance sets a lower limit on how far, in reverse KL terms, the soft-optimal policy lies from the starting policy. For binary rewards, this means prompts with a pass rate near 0.5 carry the most learning signal.

Building on this, they propose balanced online filtering for GRPO. Each prompt's pass rate is estimated from its rollouts, and only prompts inside a chosen band are kept. Asynchronous sampling keeps adding new prompts until the batch is full again. Experiments with 3B and 7B models on five math benchmarks show higher accuracy and faster convergence than plain GRPO. The analysis also extends to Gaussian and multinomial rewards, which gives a principled basis for designing RLVR curricula.

Key points

  • Core bound: D_KL(π_init‖π*) ≥ p(x)(1−p(x))/(2β²). The bound peaks at a pass rate of 0.5 and drops to zero for prompts that are always solved or always failed.
  • Batch construction: Prompts are filtered by pass-rate thresholds, for example 0.25 ≤ p(x) ≤ 0.75. Filtered-out prompts are replaced via parallel rollouts so that the batch size N stays fixed.
  • Accuracy gains: The 3B model gains +10% on AIME and +4.2% on average. The 7B model gains +12% on AMC and +4.5% on average.
  • Efficiency: Filtering surpasses plain GRPO with fewer than half the gradient updates. The narrow 0.4–0.6 band reached the highest reward but needed many more rollouts to fill each batch.
  • Generalization and limits: Viewing the reverse KL as a cumulant generating function extends the variance-based proxy to Gaussian and multinomial rewards. Empirical tests cover math reasoning only.

Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.

 Institutions

🎓Korea Advanced Institute of Science and TechnologyDaejeon · South Korea51 works · 3,167 citations

 Fields, topics and concepts

📚 Shelves 4The field of science this work belongs to (OpenAlex fields).Computer Science · 16,667 worksArtificial Intelligence · 16,194 worksArts and Humanities · 16,039 worksLanguage and Linguistics · 15,891 works

🧭 Topics 1Research subjects and languages the work is about.Reasoning · 1,426 works

Cite

Cite as Sanghwan Bae, Jiwoo Hong, Min Young Lee, Hanbyul Kim, Jeongyeon Nam and Donghyun Kwak. 2026. Online Difficulty Filtering for Reasoning Oriented Reinforcement Learning. Proceedings of the 19th Conference of the European Chapter of the Association for Computational Linguistics (Volume 1: Long Papers).

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.18653/v1/2026.eacl-long.30

@inproceedings{bae2026online,
  title = {{Online Difficulty Filtering for Reasoning Oriented Reinforcement Learning}},
  author = {Sanghwan Bae, Jiwoo Hong, Min Young Lee, Hanbyul Kim, Jeongyeon Nam and Donghyun Kwak},
  booktitle = {Proceedings of the 19th Conference of the European Chapter of the Association for Computational Linguistics (Volume 1: Long Papers)},
  year = {2026},
  doi = {10.18653/v1/2026.eacl-long.30},
  url = {https://doi.org/10.18653/v1/2026.eacl-long.30}
}

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