Token-Level Policy Optimization: Linking Group-Level Rewards to Token-Level Aggregation via Markov Likelihood

Group Relative Policy Optimization (GRPO) has significantly advanced the reasoning ability of large language models (LLMs), particularly by boosting their mathematical performance. However, GRPO and related entropy-regularization methods still face challenges rooted in the sparse token rewards inherent to chain-of-thought (CoT). Current approaches often rely on undifferentiated token-level entropy adjustments, which frequently lead to entropy collapse or model collapse. In this work, we propose TEPO, a novel token-level framework that incorporates Markov Likelihood (sequence likelihood) links group-level rewards with tokens via token-level aggregation. Experiments show that TEPO consistently outperforms existing baselines across key metrics (including @k and accuracy). It not only sets a new state of the art on mathematical reasoning tasks but also significantly enhances training stability.

Knowledgeable-r1: Policy Optimization for Knowledge Exploration in Retrieval-Augmented Generation

Retrieval-augmented generation (RAG) is a mainstream method for improving performance on knowledge-intensive tasks. However,current RAG systems often place too much emphasis on retrieved contexts. This can lead to reliance on inaccurate sources and overlook the model's inherent knowledge, especially when dealing with misleading or excessive information. To resolve this imbalance, we propose Knowledgeable-r1 that using joint sampling and define multi policy distributions in knowledge capability exploration to stimulate large language models'self-integrated utilization of parametric and contextual knowledge. Experiments show that Knowledgeable-r1 significantly enhances robustness and reasoning accuracy in both parameters and contextual conflict tasks and general RAG tasks, especially outperforming baselines by 17.07% in counterfactual scenarios and demonstrating consistent gains across RAG tasks. Our code are available at https://github.com/lcy80366872/ knowledgeable-r1.