Preference Optimization for Reasoning with Pseudo Feedback
Paper · 2024 · Fangkai Jiao, Geyang Guo, Xingxing Zhang et al.
Summary
Preference learning methods such as DPO and PPO help LLMs reason better in math and coding. However, they need reliable labels to separate good solutions from bad ones, and expert-verified reasoning data is scarce and costly to scale. The authors propose PFPO (Pseudo-Feedback Preference Optimization), which treats labeling as checking a solution against test cases. A math problem becomes a single test with empty input and the answer as output. A coding task has several input–output pairs, and a solution counts as correct only if it passes all of them.
Pseudo test cases come from two sources. The first is frontier LLMs, prompted through a multi-step decomposition. The second is the policy model itself, using majority voting over executed outputs, which extends self-consistency to problems with multiple tests. Correct and incorrect samples form DPO pairs. The two kinds of feedback are mutually reinforcing, and the procedure can be repeated over multiple rounds. With Mathstral-7B, MATH accuracy rises from 58.3 to 68.6, outperforming NuminaMath-72B and GPT-4-Turbo-1106-preview. The approach matters because it scales preference optimization without human annotation.
Key points
- Correctness score: A solution is scored by the share of test cases it passes. Only a perfect score counts as correct, so math problems get a binary 0/1 label. DPO was chosen over PPO for its simplicity.
- Self-consistency for code: The policy model writes several programs, which are run on generated test inputs. The most frequent output for each input becomes the pseudo expected output.
- Math results (Mathstral-7B base):
- MATH: 58.3 → 68.6
- GSM8K: 85.6 → 90.3
- College Math: 34.3 → 42.3
- Coding results: On Deepseek-coder-7B-v1.5, LiveCodeBench improves from 21.1 to 24.6, surpassing Claude-3-Haiku.
- Code release: Available at github.com/microsoft/unilm/tree/master/PFPO. The work was done by Fangkai Jiao et al., from NTU, Microsoft Research, A*STAR, Georgia Tech, and Salesforce.
Institutions
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 Fangkai Jiao, Geyang Guo, Xingxing Zhang, Nancy F. Chen, Shafiq Joty and Furu Wei. 2024. Preference Optimization for Reasoning with Pseudo Feedback. arXiv:2411.16345.
@misc{jiao2024preference,
title = {{Preference Optimization for Reasoning with Pseudo Feedback}},
author = {Fangkai Jiao, Geyang Guo, Xingxing Zhang, Nancy F. Chen, Shafiq Joty and Furu Wei},
year = {2024},
doi = {10.48550/arxiv.2411.16345},
eprint = {2411.16345},
archivePrefix = {arXiv},
url = {https://doi.org/10.48550/arxiv.2411.16345}
}References
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