Title: Towards demystifying the optimization landscape of RLVR methods
Primary area: foundation or frontier models, including LLMs
Keywords: Reasoning, Language Models, GRPO

Abstract: GRPO has achieved impressive success in the landscape of reasoning models. However, the motivation behind its origins along with the reasons for its effectiveness remain elusive. In this work, we fill some of the gaps and demonstrate that in on-policy setting, GRPO's optimization can be viewed as a weighted combination of maximization of likelihood for correct rollouts and minimization for the incorrect ones. This finding gives a different perspective on the optimization landscape of GRPO. Motivated by this, we analyze the positive and negative part of GRPO's objective function independently, and find that their global minima correspond to undesired solutions. While optimization of the positive term leads to entropy minimization and length collapse, optimizing for the negative term leads to entropy maximization and length explosion. Using this lens, we show the presence of instability in on-policy training of some recent algorithmic advances trying to simplify GRPO's objective. Surprisingly, we find that PPO is also susceptible to such training instabilities. However, despite the presence of bad global minima in GRPO's objective function, it doesn't converge to either of them. We identify design choices in GRPO's advantages that aid convergence of GRPO to good minima. We also demonstrate the effectiveness of using clipping in stabilizing the optimization process, thereby preventing training instabilities even when training only for minimizing the likelihood of incorrect rollouts. This highlights the surprising stability of off-policy methods as compared to using their on-policy versions.