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Group Relative Policy Optimization (GRPO) was introduced and used recently for promoting reasoning in LLMs under verifiable (binary) rewards. We show that the mean + variance calibration of these rewards induces a weighted contrastive loss…

Machine Learning · Computer Science 2025-10-22 Youssef Mroueh

GRPO is a standard approach to endowing pretrained LLMs with reasoning capabilities. It estimates the advantage of an outcome from a group of $K$ outcomes, and promotes those with positive advantages inside a trust region. Since GRPO…

Machine Learning · Computer Science 2026-02-02 Wenzheng Zhang , Karl Stratos

Group-Relative Policy Optimization (GRPO) has emerged as the standard for training reasoning capabilities in large language models through reinforcement learning. By estimating advantages using group-mean rewards rather than a learned…

Artificial Intelligence · Computer Science 2026-03-06 Anisha Garg , Claire Zhang , Nishit Neema , David Bick , Ganesh Venkatesh , Joel Hestness

The recent success and openness of DeepSeek-R1 have brought widespread attention to Group Relative Policy Optimization (GRPO) as a reinforcement learning method for large reasoning models (LRMs). In this work, we analyze the GRPO objective…

Machine Learning · Computer Science 2026-01-07 Gang Li , Ming Lin , Tomer Galanti , Zhengzhong Tu , Tianbao Yang

Reinforcement Learning with Verifiable Rewards (RLVR), primarily driven by the Group Relative Policy Optimization (GRPO) algorithm, is a leading approach for enhancing the reasoning abilities of Large Language Models (LLMs). Despite its…

Machine Learning · Computer Science 2025-10-21 Kangqi Ni , Zhen Tan , Zijie Liu , Pingzhi Li , Tianlong Chen

Reinforcement Learning with Verifiable Rewards (RLVR) has advanced the reasoning capabilities of Large Language Models (LLMs) by leveraging direct outcome verification instead of learned reward models. Building on this paradigm, Group…

Machine Learning · Computer Science 2026-04-23 Jingyi Wang , Lei Zhu , Tengjin Weng , Song-Li Wu , Haochen Tan , Jierun Chen , Chaofan Tao , Haoli Bai , Lu Hou , Lifeng Shang , Xiao-Ping Zhang

Reinforcement learning with verifiable rewards (RLVR), due to the deterministic verification, becomes a dominant paradigm for enhancing the reasoning ability of large language models (LLMs). The community witnesses the rapid change from the…

Computation and Language · Computer Science 2026-05-08 Mingwei Xu , Hao Fang

Reinforcement learning with verifiable rewards (RLVR) has become an effective paradigm for improving reasoning language models on tasks such as mathematics, coding, and scientific question answering. However, widely used group-relative…

Computation and Language · Computer Science 2026-05-29 Redacted by arXiv

Reinforcement Learning with Verifiable Rewards (RLVR) has significantly advanced the reasoning capacity of Large Language Models (LLMs). However, RLVR solely relies on final answers as outcome rewards, neglecting the correctness of…

Machine Learning · Computer Science 2026-03-12 Sijia Cui , Pengyu Cheng , Jiajun Song , Yongbo Gai , Guojun Zhang , Zhechao Yu , Jianhe Lin , Xiaoxi Jiang , Guanjun Jiang

Reinforcement Learning with Verifiable Rewards (RLVR) has improved the reasoning abilities of Large Language Models (LLMs) by using rule-based binary feedback. However, current RLVR methods typically assign the same reward to every token.…

Machine Learning · Computer Science 2025-10-21 Guofu Xie , Yunsheng Shi , Hongtao Tian , Ting Yao , Xiao Zhang

Reinforcement learning with verifiable rewards (RLVR) has emerged as the leading approach for enhancing reasoning capabilities in large language models. However, it faces a fundamental compute and memory asymmetry: rollout generation is…

Machine Learning · Computer Science 2026-04-23 Yixuan Even Xu , Yash Savani , Fei Fang , J. Zico Kolter

Reinforcement learning from verifiable rewards (RLVR), especially with Group Relative Policy Optimization (GRPO), has shown strong potential for improving the reasoning capabilities of large vision-language models (LVLMs). However, in…

Artificial Intelligence · Computer Science 2026-05-11 Bingqing Jiang , Difan Zou

Reinforcement learning with verifiable reward has recently emerged as a central paradigm for post-training large language models (LLMs); however, prevailing mean-based methods, such as Group Relative Policy Optimization (GRPO), suffer from…

Machine Learning · Computer Science 2025-10-02 Tao Ren , Jinyang Jiang , Hui Yang , Wan Tian , Minhao Zou , Guanghao Li , Zishi Zhang , Qinghao Wang , Shentao Qin , Yanjun Zhao , Rui Tao , Hui Shao , Yijie Peng

Reinforcement Learning with Verified Reward (RLVR) has emerged as a critical paradigm for advancing the reasoning capabilities of Large Language Models (LLMs). Most existing RLVR methods, such as GRPO and its variants, ensure stable updates…

Machine Learning · Computer Science 2026-02-10 Qingyuan Wu , Yuhui Wang , Simon Sinong Zhan , Yanning Dai , Shilong Deng , Sarra Habchi , Qi Zhu , Matthias Gallé , Chao Huang

Group-advantage-based reinforcement learning methods, such as GRPO and DAPO, have demonstrated strong performance across diverse domains, including mathematical reasoning and text-to-image generation. However, their reliance on sample-level…

Computer Vision and Pattern Recognition · Computer Science 2026-05-29 Shufan Li , Konstantinos Kallidromitis , Akash Gokul Yusuke Kato , Kazuki Kozuka , Aditya Grover

Diffusion large language models (dLLMs) offer a promising route to parallel and efficient text generation, but improving their reasoning ability requires effective post-training. Reinforcement learning with verifiable rewards (RLVR) is a…

Computation and Language · Computer Science 2026-05-12 Zichao Yu , Shengze Xu , Bingqing Jiang , Wenyi Zhang , Difan Zou

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a promising approach to improve the reasoning abilities of Large Language Models (LLMs). Among RLVR algorithms, Group Relative Policy Optimization (GRPO) and its variants…

Artificial Intelligence · Computer Science 2026-04-21 Zhaokang Liao , Yingguo Gao , Yi Yang , Yongheng Hu , Jingting Ding

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as an indispensable paradigm for enhancing reasoning in Large Language Models (LLMs). However, standard policy optimization methods, such as Group Relative Policy…

Machine Learning · Computer Science 2026-02-09 Pengyi Li , Elizaveta Goncharova , Andrey Kuznetsov , Ivan Oseledets

RLVR has enhanced the reasoning capabilities of Large Language Models (LLMs) across various tasks. However, GRPO, a representative RLVR algorithm, suffers from a critical limitation: when all responses within a group are either entirely…

Machine Learning · Computer Science 2025-09-24 Gongrui Nan , Siye Chen , Jing Huang , Mengyu Lu , Dexun Wang , Chunmei Xie , Weiqi Xiong , Xianzhou Zeng , Qixuan Zhou , Yadong Li , Xingzhong Xu

Recent large reasoning models (LRMs) driven by reinforcement learning algorithms (e.g., GRPO) have achieved remarkable performance on challenging reasoning tasks. However, these models suffer from overthinking, generating unnecessarily long…

Artificial Intelligence · Computer Science 2026-03-03 Gang Li , Yan Chen , Ming Lin , Tianbao Yang
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