GRPO

Group Relative Policy Optimization (GRPO): Mathematical Foundations, Group Baseline Advantage, Critic-Free Policy Gradients, and Reasoning Scaling

Reinforcement learning from human feedback (RLHF) and reinforcement learning with verifiable rewards (RLVR) have become central to post-training large language models. For years, the default policy optimization algorithm in LLM alignment was Proximal Policy Optimization (PPO). While PPO offers stable policy updates through clipped surrogate objectives and Generalized Advantage Estimation (GAE), it introduces severe computational and architectural overhead when scaled to hundred-billion-parameter