# Parameter Exploration for RLVR via Variational Learning

arXiv: https://arxiv.org/abs/2608.09805 · HTML: https://mlsanity.com/paper/2608.09805/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 76 references that are in the map.
- First posted on arXiv 10 Aug 2026.

## Builds on (most cited first, 30 of 45)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [Noisy Networks for Exploration](https://mlsanity.com/paper/1706.10295/) (2017)
- [ProRL: Prolonged Reinforcement Learning Expands Reasoning Boundaries in Large Language Models](https://mlsanity.com/paper/2505.24864/) (2025)
- [Skywork Open Reasoner 1 Technical Report](https://mlsanity.com/paper/2505.22312/) (2025)
- [The Surprising Effectiveness of Negative Reinforcement in LLM Reasoning](https://mlsanity.com/paper/2506.01347/) (2025)
- [Parameter Space Noise for Exploration](https://mlsanity.com/paper/1706.01905/) (2017)
- [Fast and Scalable Bayesian Deep Learning by Weight-Perturbation in Adam](https://mlsanity.com/paper/1806.04854/) (2018)
- [Echo Chamber: RL Post-training Amplifies Behaviors Learned in Pretraining](https://mlsanity.com/paper/2504.07912/) (2025)
- [The Bayesian Learning Rule](https://mlsanity.com/paper/2107.04562/) (2021)
- [Reasoning or Memorization? Unreliable Results of Reinforcement Learning Due to Data Contamination](https://mlsanity.com/paper/2507.10532/) (2025)
- [A Survey of Exploration Methods in Reinforcement Learning](https://mlsanity.com/paper/2109.00157/) (2021)
- [Variational Learning is Effective for Large Deep Networks](https://mlsanity.com/paper/2402.17641/) (2024)
- [e3: Learning to Explore Enables Extrapolation of Test-Time Compute for LLMs](https://mlsanity.com/paper/2506.09026/) (2025)
- [Generalized Variational Inference: Three arguments for deriving new Posteriors](https://mlsanity.com/paper/1904.02063/) (2019)

## Built on by (most cited first, 1 of 1)

- [When Does Momentum Help in Reinforcement Learning with Verifiable Rewards?](https://mlsanity.com/paper/2610.20413/) (2026)

## Abstract (arXiv)

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.