@inproceedings{lv-etal-2026-beyond-sft,
title = "Beyond {SFT}-Optimality: Cold-Start Data Selection for Reinforcement Learning via Gradient Subspace Coverage",
author = "Lv, Haisheng and
Su, Zikun and
Liu, Jingbang and
Huang, Zilu and
Liu, Xinzhang and
Deng, Wenmin and
Zhao, Yu and
Wang, Chao and
Song, Shuangyong",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.emnlp-main.513/",
pages = "11769--11789",
ISBN = "979-8-89176-459-0",
abstract = "Cold-start supervised fine-tuning (SFT) is a critical initialization step before reinforcement learning from verifiable rewards (RLVR). Yet existing cold-start data selection methods largely inherit criteria from supervised instruction tuning{---}sample quality, difficulty, perplexity, or diversity{---}implicitly assuming that a stronger SFT warm start is also a better starting point for RL. We argue that this assumption does not always hold in the SFT-to-RL pipeline: cold-start SFT not only reduces supervised loss but also shapes the initial update geometry that downstream reward optimization inherits. Building on this observation, we propose RL-Proxy-Coverage. Our method estimates a low-rank, reward-relevant gradient subspace from a small set of representative RL anchor prompts and verifier rewards, and selects, as the cold-start subset, those candidate SFT examples whose gradients provide non-redundant coverage of this subspace. In controlled mathematical-reasoning experiments, RL-Proxy-Coverage outperforms representative SFT-centric, hard-diverse, and reward-aware baselines at the early-to-mid RL checkpoints. Our findings suggest a new view of cold-start data: it should be regarded not merely as supervised examples for improving SFT, but as an initialization resource that shapes the starting point of downstream reward optimization."
}<?xml version="1.0" encoding="UTF-8"?>
<modsCollection xmlns="http://www.loc.gov/mods/v3">
<mods ID="lv-etal-2026-beyond-sft">
<titleInfo>
<title>Beyond SFT-Optimality: Cold-Start Data Selection for Reinforcement Learning via Gradient Subspace Coverage</title>
</titleInfo>
<name type="personal">
<namePart type="given">Haisheng</namePart>
<namePart type="family">Lv</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Zikun</namePart>
<namePart type="family">Su</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Jingbang</namePart>
<namePart type="family">Liu</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Zilu</namePart>
<namePart type="family">Huang</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Xinzhang</namePart>
<namePart type="family">Liu</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Wenmin</namePart>
<namePart type="family">Deng</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Yu</namePart>
<namePart type="family">Zhao</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Chao</namePart>
<namePart type="family">Wang</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Shuangyong</namePart>
<namePart type="family">Song</namePart>
<role>
<roleTerm authority="marcrelator" type="text">author</roleTerm>
</role>
</name>
<originInfo>
<dateIssued>2026-10</dateIssued>
</originInfo>
<typeOfResource>text</typeOfResource>
<relatedItem type="host">
<titleInfo>
<title>Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing</title>
</titleInfo>
<name type="personal">
<namePart type="given">Hung-Yi</namePart>
<namePart type="family">Lee</namePart>
<role>
<roleTerm authority="marcrelator" type="text">editor</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Sunipa</namePart>
<namePart type="family">Dev</namePart>
<role>
<roleTerm authority="marcrelator" type="text">editor</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Jessy</namePart>
<namePart type="family">Li</namePart>
<role>
<roleTerm authority="marcrelator" type="text">editor</roleTerm>
</role>
</name>
<name type="personal">
<namePart type="given">Desmond</namePart>
<namePart type="family">Elliott</namePart>
<role>
<roleTerm authority="marcrelator" type="text">editor</roleTerm>
</role>
</name>
<originInfo>
<publisher>Association for Computational Linguistics</publisher>
<place>
<placeTerm type="text">Budapest, Hungary</placeTerm>
</place>
</originInfo>
<genre authority="marcgt">conference publication</genre>
<identifier type="isbn">979-8-89176-459-0</identifier>
</relatedItem>
<abstract>Cold-start supervised fine-tuning (SFT) is a critical initialization step before reinforcement learning from verifiable rewards (RLVR). Yet existing cold-start data selection methods largely inherit criteria from supervised instruction tuning—sample quality, difficulty, perplexity, or diversity—implicitly assuming that a stronger SFT warm start is also a better starting point for RL. We argue that this assumption does not always hold in the SFT-to-RL pipeline: cold-start SFT not only reduces supervised loss but also shapes the initial update geometry that downstream reward optimization inherits. Building on this observation, we propose RL-Proxy-Coverage. Our method estimates a low-rank, reward-relevant gradient subspace from a small set of representative RL anchor prompts and verifier rewards, and selects, as the cold-start subset, those candidate SFT examples whose gradients provide non-redundant coverage of this subspace. In controlled mathematical-reasoning experiments, RL-Proxy-Coverage outperforms representative SFT-centric, hard-diverse, and reward-aware baselines at the early-to-mid RL checkpoints. Our findings suggest a new view of cold-start data: it should be regarded not merely as supervised examples for improving SFT, but as an initialization resource that shapes the starting point of downstream reward optimization.</abstract>
<identifier type="citekey">lv-etal-2026-beyond-sft</identifier>
<location>
<url>https://aclanthology.org/2026.emnlp-main.513/</url>
</location>
<part>
<date>2026-10</date>
<extent unit="page">
<start>11769</start>
<end>11789</end>
</extent>
</part>
</mods>
</modsCollection>
%0 Conference Proceedings
%T Beyond SFT-Optimality: Cold-Start Data Selection for Reinforcement Learning via Gradient Subspace Coverage
%A Lv, Haisheng
%A Su, Zikun
%A Liu, Jingbang
%A Huang, Zilu
%A Liu, Xinzhang
%A Deng, Wenmin
%A Zhao, Yu
%A Wang, Chao
%A Song, Shuangyong
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-459-0
%F lv-etal-2026-beyond-sft
%X Cold-start supervised fine-tuning (SFT) is a critical initialization step before reinforcement learning from verifiable rewards (RLVR). Yet existing cold-start data selection methods largely inherit criteria from supervised instruction tuning—sample quality, difficulty, perplexity, or diversity—implicitly assuming that a stronger SFT warm start is also a better starting point for RL. We argue that this assumption does not always hold in the SFT-to-RL pipeline: cold-start SFT not only reduces supervised loss but also shapes the initial update geometry that downstream reward optimization inherits. Building on this observation, we propose RL-Proxy-Coverage. Our method estimates a low-rank, reward-relevant gradient subspace from a small set of representative RL anchor prompts and verifier rewards, and selects, as the cold-start subset, those candidate SFT examples whose gradients provide non-redundant coverage of this subspace. In controlled mathematical-reasoning experiments, RL-Proxy-Coverage outperforms representative SFT-centric, hard-diverse, and reward-aware baselines at the early-to-mid RL checkpoints. Our findings suggest a new view of cold-start data: it should be regarded not merely as supervised examples for improving SFT, but as an initialization resource that shapes the starting point of downstream reward optimization.
%U https://aclanthology.org/2026.emnlp-main.513/
%P 11769-11789
Markdown (Informal)
[Beyond SFT-Optimality: Cold-Start Data Selection for Reinforcement Learning via Gradient Subspace Coverage](https://aclanthology.org/2026.emnlp-main.513/) (Lv et al., EMNLP 2026)
ACL
- Haisheng Lv, Zikun Su, Jingbang Liu, Zilu Huang, Xinzhang Liu, Wenmin Deng, Yu Zhao, Chao Wang, and Shuangyong Song. 2026. Beyond SFT-Optimality: Cold-Start Data Selection for Reinforcement Learning via Gradient Subspace Coverage. In Proceedings of the 2026 Conference on Empirical Methods in Natural Language Processing, pages 11769–11789, Budapest, Hungary. Association for Computational Linguistics.