Don't Waste Mistakes: Leveraging Negative RL-Groups via Confidence
  Reweighting
Authors: name: Yunzhen Feng, name: Parag Jain, name: Anthony Hartshorn, name: Yaqi Duan, name: Julia Kempe

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
Likelihood Estimation with Negative Samples
(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.