Group Relative Policy Optimization (GRPO) eliminates the learned critic in PPO by using the mean reward of grouped rollouts as a baseline. We provide a rigorous derivation of GRPO from first principles of the policy gradient theorem, revealing a fundamental credit assignment failure: under output-only reward, every token in a rollout receives identical advantage, collapsing token-level credit to a single scalar. We prove this induces gradient sparsity that intensifies over training, and demonstrate empirically via SVD analysis of GRPO gradients on Nemotron-4B/GSM8K that the gradient matrix has effective rank $\approx$ 2 regardless of group size $R \in \{2, 4, 8\}$. We formalize this as an intrinsic rank-2 structure arising from the zero-sum constraint on advantages and derive conditions under which GRPO's baseline is optimal. Our results characterize when GRPO's simplicity is theoretically justified and identify the credit assignment bottleneck as the key limitation for multi-step reasoning.
Reinforcement Learning (RL) has substantially improved the reasoning ability of large language models (LLMs), but sparse outcome rewards still make token-level credit assignment difficult. Existing scalable RL methods typically assign trajectory-level rewards uniformly across tok…
Group Relative Policy Optimization (GRPO) has shown strong effectiveness in reinforcement learning from verifiable feedback, where sampled rollouts can be compared within a group using task-provided correctness signals. However, extending group-relative optimization beyond verifi…
Training multi-turn evidence-reading agents with outcome-only reinforcement learning is unstable because intermediate turns receive little direct credit. In HotpotQA experiments with Qwen2.5-3B-Instruct, GRPO initially improves (standard F1 0.430) but subsequently collapses to 10…
Group Relative Policy Optimization (GRPO) is a powerful reinforcement learning algorithm for aligning generative models with human preferences. While successful in large language models~\cite{shao2024deepseekmathpushinglimitsmathematical}, its extension to diffusion and flow matc…
We formulate reinforcement learning (RL) in continuous time with discrete state spaces and possibly arbitrary action spaces via a stochastic control approach, where the state dynamics are modeled as a controlled continuous-time Markov chain (CTMC). We consider policy optimization…
The Credit Assignment Problem (CAP) is fundamental to developing efficient and explainable Reinforcement Learning (RL) agents. Existing frameworks, whether relying on temporal contiguity or hindsight-conditioned reward reweighting, frequently fail to attribute properly between an…