REINFORCE++: Stabilizing Critic-Free Policy Optimization with Global Advantage Normalization

Reinforcement Learning from Human Feedback~(RLHF) plays a crucial role in aligning Large Language Models~(LLMs). The dominant algorithm, Proximal Policy Optimization~(PPO), employs a critic network to estimate advantages, which introduces significant computational and memory overhead. To address this, a family of critic-free algorithms (e.g., GRPO, RLOO) has emerged. However, these methods typically rely on \textit{prompt-level (local)} advantage normalization, which suffers from inaccurate advantage estimation, a tendency to overfit, and, as we show, is a theoretically biased estimator. To solve these challenges, we introduce REINFORCE++, a critic-free framework centered on \textbf{Global Advantage Normalization}. By normalizing advantages across the entire global batch rather than small, prompt-specific groups, our method provides a more stable and theoretically sound, \textit{effectively unbiased} estimate (whose bias vanishes as batch size increases). We introduce two variants: REINFORCE++, a highly efficient and general algorithm ($k \ge 1$) for general-domain RLHF, and REINFORCE++ /w baseline, a robust group-sampling variant ($k > 1$) for complex reasoning tasks. Our empirical evaluation demonstrates that each variant shows superior stability and performance in its respective domain, outperforming existing methods and even PPO in complex agentic settings.