GUPO: Gradient Uncertainty-aware Policy Optimization for Post-Training Large Language Models

Post-training plays a crucial role in refining and aligning large language models to meet specific tasks and human preferences. While recent advancements in post-training techniques, such as Group Relative Policy Optimization (GRPO), leverage increased sampling with relative reward scoring to achieve superior performance, these methods often suffer from training instability that limits their practical adoption. As a next step, we present Group Variance Policy Optimization (GVPO). GVPO incorporates the analytical solution to KL-constrained reward maximization directly into its gradient weights, ensuring alignment with the optimal policy. The method provides intuitive physical interpretations: its gradient mirrors the mean squared error between the central distance of implicit rewards and that of actual rewards. GVPO offers two key advantages: (1) it guarantees a unique optimal solution, exactly the KL-constrained reward maximization objective, (2) it supports flexible sampling distributions that avoids on-policy and importance sampling limitations. By unifying theoretical guarantees with practical adaptability, GVPO establishes a new paradigm for reliable and versatile LLM post-training.

Post-training plays a pivotal role in enhancing the reasoning capabilities and task-specific expertise of large language models (LLMs). Despite recent advances in post-training methods, such as Group Relative Policy Optimization (GRPO), their practical deployment remains impeded by training instability arising from the reliance on importance sampling. We introduce Group Variance Policy Optimization (GVPO), a novel post-training method that integrates the analytical solution of KL-constrained reward maximization into its gradient weighting scheme. This formulation provides an intuitive interpretation: GVPO's gradient corresponds to the mean squared error between the central distance of implicit rewards and that of actual rewards. GVPO offers two key advantages: (1) it guarantees a unique optimal solution, exactly to the KL-constrained reward maximization objective, and (2) it enables flexible sampling distributions without requiring importance sampling. Beyond general post-training, we show that GVPO naturally extends to on-policy distillation (OPD). Furthermore, GVPO enables the optimization of a broad family of extended OPD objectives, providing a principled foundation for diverse objective design. By unifying theoretical guarantees with practical adaptability, GVPO establishes a new paradigm for reliable and versatile LLM post-training and on-policy distillation.

We identify a new dimension for enhancing rollout diversity in Group Relative Policy Optimization (GRPO) for LLMs. While GRPO relies on diverse rollouts, prevailing strategies primarily increase diversity by injecting more token-level randomness, which may introduce step-wise noise and lead to incoherent trajectories. We uncover that smaller models within the same model family inherently exhibit higher policy-level diversity, indicated by their superior pass@k relative to larger counterparts as sample counts increase. Unlike token-level noise, this diversity is temporally correlated, preserves logical consistency, and provides structured exploration signals for gradient estimation. We thus propose S2L-PO (Small-to-Large Policy Optimization), a framework that leverages fixed small models as natural explorers to train larger models. To balance exploration and exploitation, we design a progressive annealing strategy that transitions from offline small-model rollouts to the large learner's own sampling. This shift elegantly avoids mid-training performance drops caused by the small model's capacity limits, achieving faster convergence and unlocking a higher performance ceiling. S2L-PO improves accuracy on diverse mathematical reasoning benchmarks (e.g., +8.8% on AIME 24 using a 1.7B explorer to guide the 8B model) while reducing rollout compute.