No Prompt Left Behind: Exploiting Zero-Variance Prompts in LLM
  Reinforcement Learning via Entropy-Guided Advantage Shaping

Thanh-Long V. Le; Myeongho Jeon; Kim Vu; Viet Lai; Eunho Yang

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Paper · arXiv 2509.21880

No Prompt Left Behind: Exploiting Zero-Variance Prompts in LLM Reinforcement Learning via Entropy-Guided Advantage Shaping

Thanh-Long V. Le, Myeongho Jeon, Kim Vu, Viet Lai, Eunho Yang

54 upvotesSeptember 26, 2025arXiv 预印本

AI 摘要

RL-ZVP, a novel reinforcement learning algorithm, leverages zero-variance prompts to improve the accuracy and pass rate of Large Language Models in math reasoning tasks.

Reinforcement Learning with Verifiable RewardsLarge Language ModelsGRPOzero-variance promptspolicy optimizationtoken-level characteristicsmath reasoning benchmarks

Abstract

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.