No Prompt Left Behind: Exploiting Zero-Variance Prompts in LLM
  Reinforcement Learning via Entropy-Guided Advantage Shaping
Authors: name: Thanh-Long V. Le, name: Myeongho Jeon, name: Kim Vu, name: Viet Lai, name: Eunho Yang
Organization: KAIST AI

Reinforcement Learning with Verifiable Rewards (RLVR) is a powerful framework
for improving the reasoning abilities of Large Language Models (LLMs). However,
current methods such as GRPO rely only on problems where the model responses to
the same input differ in correctness, while ignoring those where all responses
receive the same reward - so-called zero-variance prompts. In this work, we
argue that such prompts are not useless but can, in fact, provide meaningful
feedback for policy optimization. To this end, we introduce RL with
Zero-Variance Prompts (RL-ZVP), a novel algorithm that extract learning signals
from zero-variance prompts. RL-ZVP directly rewards correctness and penalizes
errors even without contrasting responses, modulating feedback with token-level
characteristics to preserve informative, nuanced signals. Across six math
reasoning benchmarks, RL-ZVP achieves significant improvements of up to 8.61
points in accuracy and 7.77 points in pass rate over GRPO, while consistently
outperforming other baselines that filter out zero-variance prompts. These
results highlight the untapped potential of learning from zero-variance prompts
in RLVR.