Title: Don’t Waste Mistakes: Leveraging Negative RL-Groups via Confidence Reweighting
Primary area: learning theory
Keywords: Reinforcement Learning, RL with verifiable reward, GRPO, negative groups, theory, reward modeling

Abstract: Reinforcement learning with verifiable rewards (RLVR) has become a standard recipe for improving large language models (LLMs) on reasoning tasks, with Group Relative Policy Optimization (GRPO) widely used in practice. Yet GRPO wastes substantial compute on negative groups: groups in which no sampled response is correct yield zero advantage and thus no gradient. We ask whether negative groups can be leveraged without extra supervision. Starting from a maximum-likelihood (MLE) objective in reward modeling, we show that the MLE gradient is equivalent to a policy gradient for a modified value function. This value function adds a confidence-weighted penalty on incorrect responses, imposing larger penalties on more confident mistakes. We refer to this as **L**ikelihood **E**stimation with **N**egative **S**amples (**LENS**). LENS modifies GRPO to assign non-zero, confidence-dependent rewards to incorrect generations, making negative groups informative and converting previously wasted samples into useful gradient updates. On the MATH benchmark with Llama-3.1-8B and Qwen-2.5-3B, the proposed variant consistently outperforms GRPO baseline, with significant gains on harder items. These results demonstrate a principled and practical way to “rescue” negative groups, improving efficiency and performance in RLVR.

TL;DR: We theoretically connect reward modeling and RLVR through a likelihood lens, providing a principled framework to better leverage GRPO’s negative groups via confidence reweighting.