# P^2O: Joint Policy and Prompt Optimization

arXiv: https://arxiv.org/abs/2603.21877 · HTML: https://mlsanity.com/paper/2603.21877/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 25 of its 29 references that are in the map.
- First posted on arXiv 23 Mar 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 25 of 25)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [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)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [Kimi K2: Open Agentic Intelligence](https://mlsanity.com/paper/2507.20534/) (2025)
- [Promptbreeder: Self-Referential Self-Improvement Via Prompt Evolution](https://mlsanity.com/paper/2309.16797/) (2023)
- [GEPA: Reflective Prompt Evolution Can Outperform Reinforcement Learning](https://mlsanity.com/paper/2507.19457/) (2025)
- [Optimizing Instructions and Demonstrations for Multi-Stage Language Model Programs](https://mlsanity.com/paper/2406.11695/) (2024)
- [Learning to Reason under Off-Policy Guidance](https://mlsanity.com/paper/2504.14945/) (2025)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [ProRL: Prolonged Reinforcement Learning Expands Reasoning Boundaries in Large Language Models](https://mlsanity.com/paper/2505.24864/) (2025)
- [Llama-Nemotron: Efficient Reasoning Models](https://mlsanity.com/paper/2505.00949/) (2025)
- [Learning by Distilling Context](https://mlsanity.com/paper/2209.15189/) (2022)
- [Nemotron 3 Nano: Open, Efficient Mixture-of-Experts Hybrid Mamba-Transformer Model for Agentic Reasoning](https://mlsanity.com/paper/2512.20848/) (2025)
- [Critique-GRPO: Advancing LLM Reasoning with Natural Language and Numerical Feedback](https://mlsanity.com/paper/2506.03106/) (2025)
- [Outcome-based Exploration for LLM Reasoning](https://mlsanity.com/paper/2509.06941/) (2025)
- [BREAD: Branched Rollouts from Expert Anchors Bridge SFT & RL for Reasoning](https://mlsanity.com/paper/2506.17211/) (2025)
- [Every Step Evolves: Scaling Reinforcement Learning for Trillion-Scale Thinking Model](https://mlsanity.com/paper/2510.18855/) (2025)
- [ExGRPO: Learning to Reason from Experience](https://mlsanity.com/paper/2510.02245/) (2025)
- [QuestA: Expanding Reasoning Capacity in LLMs via Question Augmentation](https://mlsanity.com/paper/2507.13266/) (2025)
- [GHPO: Adaptive Guidance for Stable and Efficient LLM Reinforcement Learning](https://mlsanity.com/paper/2507.10628/) (2025)
- [Adaptive Guidance Accelerates Reinforcement Learning of Reasoning Models](https://mlsanity.com/paper/2506.13923/) (2025)

## Built on by (most cited first, 3 of 3)

- [WHALE: A Simple Recipe for Joint Harness-Weight Optimization](https://mlsanity.com/paper/2609.00196/) (2026)
- [Mechanistically Interpreting the Role of Sample Difficulty in RLVR for LLMs](https://mlsanity.com/paper/2605.28388/) (2026)
- [From Existing Methods to New Research Ideas: Two Perspectives on Recursive Self-Improvement](https://mlsanity.com/paper/2610.14625/) (2026)

## Abstract (arXiv)

Reinforcement Learning with Verifiable Rewards (RLVR) enhances Large Language Model (LLM) reasoning but is suffer from advantage collapse: when all rollouts of a query receive identical rewards, the group variance vanishes, most damagingly on hard samples, where scaling rollout budgets yields little. We introduce Joint Policy and Prompt Optimization (P O) to mitigate this collapse by alternating continuous policy updates with discrete prompt evolution. P O mines hard samples with a success-rate threshold, evolves reasoning prompts for them with GEPA, and internalizes the elicited trajectories via context distillation, which optimizes each trajectory under the original query and thus removes inference-time prompting, with a Context Ratio Mask (CRM) filtering out extreme likelihood ratios. P O restores critical advantage signals and surpasses the GRPO baseline by up to 8.2 points in average accuracy on six held-out benchmarks across all training datasets and backbones, while also outperforming DAPO and other baselines. The gains are especially pronounced on hard benchmarks, reaching up to 16.3 points above GRPO on average across AIME24 and AIME25. Our findings expose the limits of standard exploration in sparse-reward environments, illuminating the potential of unifying evolutionary algorithms with reinforcement learning. This integration of discrete semantic search and continuous parameter updates provides a self-reinforcing framework that facilitates more effective LLM alignment.