Double-Rollout Reinforcement Learning with Sampling-based Reward Estimation

Abstract

Reinforcement learning with verifiable rewards (RLVR) implemented with Group Relative Policy Optimization (GRPO) has driven substantial progress in training reasoning language models. However, verifiable outcome rewards provide an imperfect measure of reasoning quality: a correct final answer may not be supported by the reasoning trace, whereas an incorrect rollout may contain a nearly correct reasoning trajectory. We present empirical evidence for this mismatch and hypothesize that the resulting reward noise contributes to instability in reinforcement learning for both reasoning accuracy and token efficiency. To address this credit assignment challenge, this paper proposes double-rollout reinforcement learning. For each sampled rollout, we truncate its reasoning trace, sample multiple continuations from the truncated prefix, and replace the original reward with the mean continuation reward, yielding a more robust estimate of reasoning quality. This double-rollout algorithm incurs only a moderate increase in compute cost and yet reaches substantially higher accuracies across math and coding tasks and across Qwen and Nemotron models than baseline algorithms with fewer RL steps. For example, using only DAPO data it trains Nemotron-3-Nano-30B-A3B to reach 95.4% on AIME 2026, versus 91.5% by GRPO and substantially above state of the art for this model size, within 30 RL steps. When combined with length-based rewards, the same algorithm further improves the accuracy-efficiency Pareto frontier over existing efficiency optimizations. These findings suggest that the double-rollout reward estimation is an effective and cost-efficient way to improve both the accuracy and token efficiency of reasoning RL.