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When Does External Guidance Help LLM Reasoning? A Bias-Variance Theory of Guidance-Augmented GRPO — arXiv:2610.06861

Source

arXiv (en)

Original

https://arxiv.org/abs/2610.06861

License (as archived)

CC0-1.0

Archived

2026-10-07T11:23:33.758Z

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f76116d4fdff9ad5b32fe712b37c34b99a67e4b219ffd6a8f2b0e4aa41d3e14f

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When Does External Guidance Help LLM Reasoning? A Bias-Variance Theory of Guidance-Augmented GRPO — arXiv:2610.06861 — arXiv (en), https://arxiv.org/abs/2610.06861 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_d1d940468a84 (Metraipolis archive dc_d1d940468a84, sha256 f76116d4fdff9ad5b32fe712b37c34b99a67e4b219ffd6a8f2b0e4aa41d3e14f)

@misc{dcd1d940468a84,
  title = {When Does External Guidance Help LLM Reasoning? A Bias-Variance Theory of Guidance-Augmented GRPO — arXiv:2610.06861},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.06861},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_d1d940468a84; sha256 f76116d4fdff9ad5b32fe712b37c34b99a67e4b219ffd6a8f2b0e4aa41d3e14f},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.06861. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Reinforcement learning with verifiable rewards (RLVR) has become the dominant paradigm for eliciting multi-step reasoning in large language models, and a recent wave of methods (LUFFY, ExPO, PAPO, TAPO) further augments RL with \emph{external guidance} - expert traces, self-explanations, or retrieved thought patterns. Although each method reports empirical gains, none provides convergence rates, bias bounds, or an optimal weighting rule for the guidance signal. We close this gap with \emph{Guidance-Augmented GRPO} (GA-GRPO), a unified theoretical framework that casts external guidance as a stochastic guidance operator G re-writing the question distribution, and analyses the resulting policy-gradient estimator as a biased on-policy estimator whose bias is bounded by the total-variation guidance divergence delta\_G between the guidance-augmented sampling distribution and the policy's own distribution. The framework subsumes vanilla GRPO, LUFFY, ExPO, PAPO, and TAPO as special cases obtained by particular choices of G. Under smoothness and bounded-divergence assumptions we prove that GA-GRPO converges at rate O(1/sqrt(T)) to an O(delta sqrt(T))-neighbourhood of the GRPO stationary point, derive the closed-form MSE-optimal guidance weight lambda-star(T, delta, sigma\_0 squared) = sigma\_0 squared / (sigma\_0 squared + R\_max squared delta squared T), and prove a matching minimax lower bound showing the Omega(delta squared T) bias term is unavoidable. Experiments on Qwen2.5-Math-7B-Base across nine math and OOD benchmarks confirm that optimal-weight GA-GRPO matches or surpasses TAPO, LUFFY, ExPO, and vanilla GRPO while requiring 31\% fewer GPU-hours, and eight analysis experiments validate each theoretical prediction.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.CL, nuovi lavori del giorno).
Categorie arXiv: Machine Learning (cs.LG) ; Computation and Language (cs.CL).
Pagina del lavoro: https://arxiv.org/abs/2610.06861 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-07T11:15:39.470Z dalla pagina https://arxiv.org/list/cs.CL/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).