GRPO-λ: Credit Assignment improves LLM Reasoning

Large language models (LLMs) are increasingly deployed for tasks requiring complex reasoning, prompting significant interest in improving their reasoning abilities through post-training. Especially RL based methods using verifiable reward, like the state-of-the-art GRPO, have shown to tremendously improve reasoning behaviors when applied as post-training methods. However, the lack of an explicit reward or critic model limits GRPO's ability to assign fine-grained credit across token sequences. In this work, we present GRPO-λ, a novel extension to GRPO that enhances credit assignment in RL finetuning of LLMs for complex reasoning tasks. We approximate learning from λ-return with a reformulation of eligibility traces using token-level log-probabilities applied after each sequence generation, and a novel critic-free approximation of the temporal-difference error. We introduce a few variations for the weighting of the λ-return, and their applications to the eligibility-trace, where all the variations provide significant gains over GRPO. We compare GRPO-λ against GRPO by training models from 1.5B to 7B parameters on 4 different math reasoning datasets. The training plots demonstrate 30-40% improved performance during RL training on both LLaMA-3.1 and Qwen-2.5 architectures. Finally, we show that with GRPO-λ, the resulting average performance on AIME24, Math500, OlympiadMath, MinervaMath, and AMC improves over GRPO by over 3 points and a 4.5 points improvement on the 7B model.