No Prompt Left Behind: Exploiting Zero-Variance Prompts in LLM Reinforcement Learning via Entropy-Guided Advantage Shaping
This addresses a bottleneck in RLVR for LLMs by utilizing previously discarded data, offering incremental but specific gains in reasoning tasks.
The paper tackled the problem of ignoring zero-variance prompts in reinforcement learning for large language models, and introduced RL-ZVP, which extracts learning signals from such prompts, achieving improvements of up to 8.61 points in accuracy and 7.77 points in pass rate over GRPO on math reasoning benchmarks.
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.