P^2O: Joint Policy and Prompt Optimization

Abstract: Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a powerful paradigm for enhancing the reasoning capabilities of LLMs. However, vanilla RLVR suffers from inefficient exploration, particularly when confronting "hard samples" that yield nearzero success rates. In such scenarios, the reliance on sparse outcome rewards typically results in zero-advantage estimates, effectively starving the model of supervision signals despite the high informational value of these instances. To address this, we propose P^2O, a novel framework that synergizes Prompt Optimization with Policy Optimization. P^2O identifies hard samples during training iterations and leverages the GeneticPareto (GEPA) prompt optimization algorithm to evolve prompt templates that guide the model toward discovering successful trajectories. Crucially, unlike traditional prompt engineering methods that rely on input augmentation, P^2O distills the reasoning gains induced by these optimized prompts directly into the model parameters. This mechanism provides denser positive supervision signals for hard samples and accelerates convergence. Extensive experiments demonstrate that P^2O not only achieves superior performance on in-distribution datasets but also exhibits strong generalization, yielding substantial improvements on out-of-distribution benchmarks (+4.7% avg.).