Free Process Rewards without Process Labels

Lifan Yuan, Wendi Li, Huayu Chen, Ganqu Cui, Ning Ding, Kaiyan Zhang, Bowen Zhou, Zhiyuan Liu, Hao Peng
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:73511-73525, 2025.

Abstract

Different from its counterpart outcome reward models (ORMs), which evaluate the entire responses, a process reward model (PRM) scores a reasoning trajectory step by step, providing denser and more fine-grained rewards. However, training a PRM requires labels annotated at every intermediate step, presenting significant challenges for both manual and automatic data collection. This paper aims to address this challenge. Both theoretically and empirically, we show that an implicit PRM can be obtained at no additional cost, by simply training an ORM on the cheaper response-level labels. The only assumption is to parameterize the outcome reward as the log-likelihood ratios of the policy and reference models r$\phi$(y) = $\beta$ log $\pi$$\phi$(y) $\pi$ref(y) , which can be optimized regardless of the specific choice of loss objectives. In experiments, we instantiate our implicit PRMs with various objectives and evaluate their performance on MATH. We show that our implicit PRM outperforms a strong MCTS-based baseline á la Math-Shepherd (Wang et al., 2023) using less than 1/38 of the training data. Its performance can be further improved with majority voting. We further find that scaling up instructions and responses benefits our implicit PRM, and the latter brings a larger gain. Particularly, we find that our implicit PRM, when instantiated with the cross-entropy (CE) loss, is more data-efficient and can keep improving generation models even when trained with only one response per instruction, the setup that suffers from extreme data scarcity and imbalance. Further, instructions should be relevant to downstream tasks while the diversity of responses does not bring gains. Surprisingly, training on extra Math-Shepherd step labels brings no further improvements to our implicit PRM trained on only outcome data. We hope that our work will encourage a rethinking of PRM training approaches and contribute to making training PRMs more accessible.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-yuan25c, title = {Free Process Rewards without Process Labels}, author = {Yuan, Lifan and Li, Wendi and Chen, Huayu and Cui, Ganqu and Ding, Ning and Zhang, Kaiyan and Zhou, Bowen and Liu, Zhiyuan and Peng, Hao}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {73511--73525}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/yuan25c/yuan25c.pdf}, url = {https://proceedings.mlr.press/v267/yuan25c.html}, abstract = {Different from its counterpart outcome reward models (ORMs), which evaluate the entire responses, a process reward model (PRM) scores a reasoning trajectory step by step, providing denser and more fine-grained rewards. However, training a PRM requires labels annotated at every intermediate step, presenting significant challenges for both manual and automatic data collection. This paper aims to address this challenge. Both theoretically and empirically, we show that an implicit PRM can be obtained at no additional cost, by simply training an ORM on the cheaper response-level labels. The only assumption is to parameterize the outcome reward as the log-likelihood ratios of the policy and reference models r$\phi$(y) = $\beta$ log $\pi$$\phi$(y) $\pi$ref(y) , which can be optimized regardless of the specific choice of loss objectives. In experiments, we instantiate our implicit PRMs with various objectives and evaluate their performance on MATH. We show that our implicit PRM outperforms a strong MCTS-based baseline á la Math-Shepherd (Wang et al., 2023) using less than 1/38 of the training data. Its performance can be further improved with majority voting. We further find that scaling up instructions and responses benefits our implicit PRM, and the latter brings a larger gain. Particularly, we find that our implicit PRM, when instantiated with the cross-entropy (CE) loss, is more data-efficient and can keep improving generation models even when trained with only one response per instruction, the setup that suffers from extreme data scarcity and imbalance. Further, instructions should be relevant to downstream tasks while the diversity of responses does not bring gains. Surprisingly, training on extra Math-Shepherd step labels brings no further improvements to our implicit PRM trained on only outcome data. We hope that our work will encourage a rethinking of PRM training approaches and contribute to making training PRMs more accessible.} }
Endnote
%0 Conference Paper %T Free Process Rewards without Process Labels %A Lifan Yuan %A Wendi Li %A Huayu Chen %A Ganqu Cui %A Ning Ding %A Kaiyan Zhang %A Bowen Zhou %A Zhiyuan Liu %A Hao Peng %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-yuan25c %I PMLR %P 73511--73525 %U https://proceedings.mlr.press/v267/yuan25c.html %V 267 %X Different from its counterpart outcome reward models (ORMs), which evaluate the entire responses, a process reward model (PRM) scores a reasoning trajectory step by step, providing denser and more fine-grained rewards. However, training a PRM requires labels annotated at every intermediate step, presenting significant challenges for both manual and automatic data collection. This paper aims to address this challenge. Both theoretically and empirically, we show that an implicit PRM can be obtained at no additional cost, by simply training an ORM on the cheaper response-level labels. The only assumption is to parameterize the outcome reward as the log-likelihood ratios of the policy and reference models r$\phi$(y) = $\beta$ log $\pi$$\phi$(y) $\pi$ref(y) , which can be optimized regardless of the specific choice of loss objectives. In experiments, we instantiate our implicit PRMs with various objectives and evaluate their performance on MATH. We show that our implicit PRM outperforms a strong MCTS-based baseline á la Math-Shepherd (Wang et al., 2023) using less than 1/38 of the training data. Its performance can be further improved with majority voting. We further find that scaling up instructions and responses benefits our implicit PRM, and the latter brings a larger gain. Particularly, we find that our implicit PRM, when instantiated with the cross-entropy (CE) loss, is more data-efficient and can keep improving generation models even when trained with only one response per instruction, the setup that suffers from extreme data scarcity and imbalance. Further, instructions should be relevant to downstream tasks while the diversity of responses does not bring gains. Surprisingly, training on extra Math-Shepherd step labels brings no further improvements to our implicit PRM trained on only outcome data. We hope that our work will encourage a rethinking of PRM training approaches and contribute to making training PRMs more accessible.
APA
Yuan, L., Li, W., Chen, H., Cui, G., Ding, N., Zhang, K., Zhou, B., Liu, Z. & Peng, H.. (2025). Free Process Rewards without Process Labels. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:73511-73525 Available from https://proceedings.mlr.press/v267/yuan25c.html.

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