Title: WS-GRPO: Weakly-Supervised Group-Relative Policy Optimization
Primary area: foundation or frontier models, including LLMs
Keywords: Weak Supervision, Large Language Models, Group Relative Policy Optimization

Abstract: Group-Relative Policy Optimization (GRPO) has emerged as an effective approach for training language models on complex reasoning tasks by normalizing rewards within groups of rollouts. 
However, GRPO's group-relative advantage estimation critically depends on dense step-wise reward signals throughout the reasoning process. 
In practice, obtaining such dense supervision requires expensive human annotations of intermediate reasoning steps or carefully designed step-wise reward functions. 
This creates a significant challenge specific to group-relative methods: while GRPO performs best with dense intermediate feedback, 
real-world scenarios often provide only sparse outcome supervision—such as final answer correctness or binary trajectory labels.
We propose Weakly-Supervised Group-Relative Policy Optimization (WS-GRPO), 
which addresses this unique limitation by learning to extract dense preference signals from sparse outcome supervision while preserving GRPO's group-relative normalization benefits. 
WS-GRPO operates in two phases: first, it trains a preference model to distinguish between successful and unsuccessful reasoning patterns using only trajectory-level outcomes; 
second, it leverages this learned preference model to provide step-wise weakly-supervised rewards that are combined with sparse terminal rewards during group-relative policy optimization. 
By treating consecutive partial trajectories as preference pairs, our method generates dense feedback signals that complement GRPO's group normalization mechanism without requiring step-by-step human annotations.
Theoretically, we provide comprehensive guarantees for WS-GRPO establishing preference model consistency under trajectory-level supervision, policy robustness to preference errors with controllable degradation rates, and generalization bounds that decompose error sources across policy learning, preference modeling, and their interaction. Our experiments on reasoning benchmarks demonstrate that WS-GRPO achieves competitive performance using only weak supervision, making group-relative policy optimization practical when detailed process supervision is limited.

TL;DR: WS-GRPO learns to extract dense step-wise rewards from sparse outcome supervision by training a preference model on trajectory pairs, enabling effective group-relative policy optimization without expensive intermediate annotations.