# Learning with a Single Rollout via Pass@k Policy Optimization

arXiv: https://arxiv.org/abs/2606.25451 · HTML: https://mlsanity.com/paper/2606.25451/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 38 references that are in the map.
- First posted on arXiv 24 Jun 2026.

## Builds on (most cited first, 30 of 32)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Process Reinforcement through Implicit Rewards](https://mlsanity.com/paper/2502.01456/) (2025)
- [Group-in-Group Policy Optimization for LLM Agent Training](https://mlsanity.com/paper/2505.10978/) (2025)
- [Mixture-of-Agents Enhances Large Language Model Capabilities](https://mlsanity.com/paper/2406.04692/) (2024)
- [Rewarding Progress: Scaling Automated Process Verifiers for LLM Reasoning](https://mlsanity.com/paper/2410.08146/) (2024)
- [ProRL: Prolonged Reinforcement Learning Expands Reasoning Boundaries in Large Language Models](https://mlsanity.com/paper/2505.24864/) (2025)
- [Beyond Benchmarks: MathArena as an Evaluation Platform for Mathematics with LLMs](https://mlsanity.com/paper/2605.00674/) (2026)
- [ARPO:End-to-End Policy Optimization for GUI Agents with Experience Replay](https://mlsanity.com/paper/2505.16282/) (2025)
- [AgentPRM: Process Reward Models for LLM Agents via Step-Wise Promise and Progress](https://mlsanity.com/paper/2511.08325/) (2025)
- [SPA-RL: Reinforcing LLM Agents via Stepwise Progress Attribution](https://mlsanity.com/paper/2505.20732/) (2025)
- [TreePO: Bridging the Gap of Policy Optimization and Efficacy and Inference Efficiency with Heuristic Tree-based Modeling](https://mlsanity.com/paper/2508.17445/) (2025)
- [Hierarchy-of-Groups Policy Optimization for Long-Horizon Agentic Tasks](https://mlsanity.com/paper/2602.22817/) (2026)
- [Information Gain-based Policy Optimization: A Simple and Effective Approach for Multi-Turn Search Agents](https://mlsanity.com/paper/2510.14967/) (2025)
- [MCPMark: A Benchmark for Stress-Testing Realistic and Comprehensive MCP Use](https://mlsanity.com/paper/2509.24002/) (2025)
- [Exploiting Tree Structure for Credit Assignment in RL Training of LLMs](https://mlsanity.com/paper/2509.18314/) (2025)
- [OneMillion-Bench: How Far are Language Agents from Human Experts?](https://mlsanity.com/paper/2603.07980/) (2026)
- [Native Parallel Reasoner: Reasoning in Parallelism via Self-Distilled Reinforcement Learning](https://mlsanity.com/paper/2512.07461/) (2025)
- [The AI Hippocampus: How Far are We From Human Memory?](https://mlsanity.com/paper/2601.09113/) (2026)

## Abstract (arXiv)

Group Relative Policy Optimization (GRPO) typically requires multiple rollouts per prompt to estimate relative credit, incurring substantial sampling cost and exacerbating training asynchrony. This limitation is particularly severe for scientific reasoning agents, where each trajectory may involve long-horizon reasoning, multiple turns, and parallel sub-runs. We study single-rollout reinforcement learning, where only one rollout is collected per prompt, and find that naive training can stagnate or become severely unstable. We introduce Single-Rollout Pass@k Policy Optimization (SR-PPO), which combines Monte Carlo token-level advantage estimation with Pass@k gradient reweighting. An online critic without large-scale pretraining is used both as a prefix-dependent baseline for credit assignment and to estimate the Pass@k gradient weight. Using only one rollout per prompt, SR-PPO achieves stable learning and performance comparable to GRPO across reasoning and logic benchmarks, even under off-policy drift that degrades the performance of standard Pass@1 PPO. A key factor in this stability is Pass@k reweighting, which emphasizes harder prompts while downweighting high-success prompts, for which imperfect credit estimates tend to produce noisier policy updates. Through analyses of critic quality, gradient noise, and update behavior, we investigate how Pass@k reweighting stabilizes single-rollout learning and why residual critic errors may limit SR-PPO's ability to outperform GRPO.