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        <title>Do Not Step Into the Same River Twice: Learning to Reason from Trial and Error</title>
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    <abstract>Reinforcement learning with verifiable rewards (RLVR) has significantly boosted the reasoning capability of language models (LMs). However, existing RLVR approaches train LMs based on their own on-policy responses and are constrained by the initial capability of LMs, thus prone to exploration stagnation, in which LMs fail to solve more training problems and cannot further learn from the training data. Some approaches try to address this by leveraging off-policy solutions to training problems, but rely on external expert guidance that is limited in availability and scalability. In this work, we propose LTE (Learning to reason from Trial and Error), an approach that hints LMs with their previously self-made mistakes, not requiring any external expert guidance. Experiments validate the effectiveness of LTE, which outperforms the normal group relative policy optimization (GRPO) by 5.02 in Pass@1 and 9.96 in Pass@k on average across six mathematical reasoning benchmarks for Qwen3-8B-Base and even performs better than methods that require external guidance. Further analysis confirms that LTE successfully mitigates exploration stagnation and enhances both exploitation and exploration during training. Our code is available at https://github.com/JamyDon/LTE.</abstract>
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%0 Conference Proceedings
%T Do Not Step Into the Same River Twice: Learning to Reason from Trial and Error
%A Tang, Chenming
%A Huang, Hsiu-Yuan
%A Liu, Weijie
%A Bai, Clive
%A Yang, Saiyong
%A Wu, Yunfang
%Y Liakata, Maria
%Y Moreira, Viviane P.
%Y Zhang, Jiajun
%Y Jurgens, David
%S Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)
%D 2026
%8 July
%I Association for Computational Linguistics
%C San Diego, California, United States
%@ 979-8-89176-390-6
%F tang-etal-2026-step
%X Reinforcement learning with verifiable rewards (RLVR) has significantly boosted the reasoning capability of language models (LMs). However, existing RLVR approaches train LMs based on their own on-policy responses and are constrained by the initial capability of LMs, thus prone to exploration stagnation, in which LMs fail to solve more training problems and cannot further learn from the training data. Some approaches try to address this by leveraging off-policy solutions to training problems, but rely on external expert guidance that is limited in availability and scalability. In this work, we propose LTE (Learning to reason from Trial and Error), an approach that hints LMs with their previously self-made mistakes, not requiring any external expert guidance. Experiments validate the effectiveness of LTE, which outperforms the normal group relative policy optimization (GRPO) by 5.02 in Pass@1 and 9.96 in Pass@k on average across six mathematical reasoning benchmarks for Qwen3-8B-Base and even performs better than methods that require external guidance. Further analysis confirms that LTE successfully mitigates exploration stagnation and enhances both exploitation and exploration during training. Our code is available at https://github.com/JamyDon/LTE.
%U https://aclanthology.org/2026.acl-long.363/
%P 8018-8032

Markdown (Informal)

[Do Not Step Into the Same River Twice: Learning to Reason from Trial and Error](https://aclanthology.org/2026.acl-long.363/) (Tang et al., ACL 2026)

• Do Not Step Into the Same River Twice: Learning to Reason from Trial and Error (Tang et al., ACL 2026)

ACL

• Chenming Tang, Hsiu-Yuan Huang, Weijie Liu, Clive Bai, Saiyong Yang, and Yunfang Wu. 2026. Do Not Step Into the Same River Twice: Learning to Reason from Trial and Error. In Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 8018–8032, San Diego, California, United States. Association for Computational Linguistics.