DiPO: Disentangled Perplexity Policy Optimization for Fine-grained Exploration-Exploitation Trade-Off

Reinforcement Learning with Verifiable Rewards (RLVR) has become a widely adopted technique for enhancing the reasoning ability of Large Language Models (LLMs). However, the effectiveness of RLVR strongly depends on the capability of base models. This issue arises because it requires the model to have sufficient capability to perform high-quality exploration, which involves both effectiveness and diversity. Unfortunately, existing methods address this issue by imitating expert trajectories, which improve effectiveness but neglect diversity. To address this, we argue that the expert only needs to provide guidance only at critical decision points rather than the entire reasoning path. Based on this insight, we propose MENTOR: Mixed-policy Expert Navigation for Token-level Optimization of Reasoning, a framework that provides expert guidance only at critical decision points to perform effective and diverse exploration in RLVR. Extensive experiments show that MENTOR enables models capture the essence of expert strategies rather than surface imitation, thereby performing high-quality exploration and achieving superior overall performance. Our code is available online.

Exploration has been a focus of reinforcement learning research for a long time. Recently, there has been growing evidence that it is also an important ingredient in LLM reinforcement learning recipes that can significantly impact downstream performance. Many existing methods control exploration in the action-space, for example, using temperature scaling. However, these methods cannot reorder tokens but only influence the variance in the output distribution. This limits exploration and can lead to divergence or stalled training. Here, we investigate parameter-space exploration, where rollouts are generated by sampling different policies from a posterior that may each explore different rollouts. Sampling less or more diverse policies is then a complementary control lever over exploration. We introduce a family of methods called Perturbed Parameter Policy Optimization (3PO) which use different sampling strategies and different rollout grouping for reward estimation. Experiments on OLMo-3-1025-7B and Qwen2.5-Math-7B across mathematical reasoning and code generation tasks show that these approaches consistently improve average downstream performance over standard GRPO at a near-identical FLOPs cost. Moreover, using multiple parameter samples consistently produces fewer zero-advantage groups and malformed or incorrect rollouts during training than GRPO and action-space baselines. Overall, our work presents evidence that parameter-space exploration can improve reinforcement learning for LLMs.

Reinforcement Learning with Verifiable Rewards (RLVR) significantly improves LLM reasoning but often causes a drop in policy entropy, leading to narrowed reasoning coverage and degraded pass@$k$ for large $k$. While existing methods mitigate this entropy collapse through algorithmic regularizations, cross-model non-parametric perturbation is also neglected. In this work, we propose a simple yet effective approach to preserve the generative diversity of LLMs during RLVR. Instead of relying solely on internal exploration, we force the target model to generate answers based on partial reasoning trajectories generated by a smaller, weaker language models. These unfamiliar prefixes effectively disrupt over-confidence and encourage the exploration of distinct reasoning paths. We empirically study the potential of outer prefixes, revealing the mechanism of the impact of distributional discrepancy to the exploration dynamics in RLVR training. Experiments across multiple mathematical benchmarks show that our method consistently outperforms vanilla RLVR. Notably, the performance gain becomes increasingly pronounced as $k$ scales up, demonstrating a substantial expansion of reasoning coverage. Furthermore, our approach efficiently mitigates entropy collapse without requiring additional SFT, intricate reward designs, or complex prompting.