On the Policy Gradient Foundations of Group Relative Policy Optimization: Credit Assignment, Gradient Sparsity, and Rank Collapse

arXiv:2606.29238v1 Announce Type: new Abstract: 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 o

Source: arXiv cs.LG — read the full report at the original publisher.

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