@inproceedings{li-etal-2026-forge,
title = "Forge: Quality-Aware Reinforcement Learning for {NP}-Hard Optimization in {LLM}s",
author = "Li, Xiaozhe and
Fang, Xinyu and
Ding, Shengyuan and
Li, Yang and
Li, Linyang and
Duan, Haodong and
Liu, Qingwen and
Chen, Kai",
editor = "Liakata, Maria and
Moreira, Viviane P. and
Zhang, Jiajun and
Jurgens, David",
booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {ACL} 2026",
month = jul,
year = "2026",
address = "San Diego, California, United States",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.findings-acl.1413/",
pages = "28351--28368",
ISBN = "979-8-89176-395-1",
abstract = "Large Language Models (LLMs) have achieved remarkable success on reasoning benchmarks through Reinforcement Learning with Verifiable Rewards (RLVR), excelling at tasks such as math, coding, logic and puzzles. However, existing benchmarks evaluate only correctness, overlooking optimality{---}the ability to find the best solutions under constraints. We propose , the first comprehensive framework for training and evaluating LLMs on NP-hard optimization problems through quality-aware RLVR. provides three key components: a scalable training infrastructure with instance generators, quality verifiers, and optimal baselines across 10 tasks; a rigorous benchmark with 1,000 instances evaluating both feasibility (Success Rate) and quality (Quality Ratio); and quality-aware rewards enabling continuous improvement beyond binary correctness. Training on Qwen2.5-7B-Instruct-1M with 15K examples achieves 93.1{\%} SR and 46.6{\%} QR, significantly outperforming GPT-4o (29.6{\%} SR, 14.6{\%} QR). Beyond optimization, training on transfers to diverse tasks: mathematics (+2.2{\%}), logic (+1.2{\%}), knowledge (+4.1{\%}), and instruction-following (+6.1{\%}). Our analysis reveals quality-aware rewards improve solutions by 28.8{\%} over binary rewards, and task diversity drives generalization more than data quantity{---}offering insights into RLVR scaling for complex reasoning."
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<abstract>Large Language Models (LLMs) have achieved remarkable success on reasoning benchmarks through Reinforcement Learning with Verifiable Rewards (RLVR), excelling at tasks such as math, coding, logic and puzzles. However, existing benchmarks evaluate only correctness, overlooking optimality—the ability to find the best solutions under constraints. We propose , the first comprehensive framework for training and evaluating LLMs on NP-hard optimization problems through quality-aware RLVR. provides three key components: a scalable training infrastructure with instance generators, quality verifiers, and optimal baselines across 10 tasks; a rigorous benchmark with 1,000 instances evaluating both feasibility (Success Rate) and quality (Quality Ratio); and quality-aware rewards enabling continuous improvement beyond binary correctness. Training on Qwen2.5-7B-Instruct-1M with 15K examples achieves 93.1% SR and 46.6% QR, significantly outperforming GPT-4o (29.6% SR, 14.6% QR). Beyond optimization, training on transfers to diverse tasks: mathematics (+2.2%), logic (+1.2%), knowledge (+4.1%), and instruction-following (+6.1%). Our analysis reveals quality-aware rewards improve solutions by 28.8% over binary rewards, and task diversity drives generalization more than data quantity—offering insights into RLVR scaling for complex reasoning.</abstract>
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%0 Conference Proceedings
%T Forge: Quality-Aware Reinforcement Learning for NP-Hard Optimization in LLMs
%A Li, Xiaozhe
%A Fang, Xinyu
%A Ding, Shengyuan
%A Li, Yang
%A Li, Linyang
%A Duan, Haodong
%A Liu, Qingwen
%A Chen, Kai
%Y Liakata, Maria
%Y Moreira, Viviane P.
%Y Zhang, Jiajun
%Y Jurgens, David
%S Findings of the Association for Computational Linguistics: ACL 2026
%D 2026
%8 July
%I Association for Computational Linguistics
%C San Diego, California, United States
%@ 979-8-89176-395-1
%F li-etal-2026-forge
%X Large Language Models (LLMs) have achieved remarkable success on reasoning benchmarks through Reinforcement Learning with Verifiable Rewards (RLVR), excelling at tasks such as math, coding, logic and puzzles. However, existing benchmarks evaluate only correctness, overlooking optimality—the ability to find the best solutions under constraints. We propose , the first comprehensive framework for training and evaluating LLMs on NP-hard optimization problems through quality-aware RLVR. provides three key components: a scalable training infrastructure with instance generators, quality verifiers, and optimal baselines across 10 tasks; a rigorous benchmark with 1,000 instances evaluating both feasibility (Success Rate) and quality (Quality Ratio); and quality-aware rewards enabling continuous improvement beyond binary correctness. Training on Qwen2.5-7B-Instruct-1M with 15K examples achieves 93.1% SR and 46.6% QR, significantly outperforming GPT-4o (29.6% SR, 14.6% QR). Beyond optimization, training on transfers to diverse tasks: mathematics (+2.2%), logic (+1.2%), knowledge (+4.1%), and instruction-following (+6.1%). Our analysis reveals quality-aware rewards improve solutions by 28.8% over binary rewards, and task diversity drives generalization more than data quantity—offering insights into RLVR scaling for complex reasoning.
%U https://aclanthology.org/2026.findings-acl.1413/
%P 28351-28368
Markdown (Informal)
[Forge: Quality-Aware Reinforcement Learning for NP-Hard Optimization in LLMs](https://aclanthology.org/2026.findings-acl.1413/) (Li et al., Findings 2026)
ACL
- Xiaozhe Li, Xinyu Fang, Shengyuan Ding, Yang Li, Linyang Li, Haodong Duan, Qingwen Liu, and Kai Chen. 2026. Forge: Quality-Aware Reinforcement Learning for NP-Hard Optimization in LLMs. In Findings of the Association for Computational Linguistics: ACL 2026, pages 28351–28368, San Diego, California, United States. Association for Computational Linguistics.