Abstract
Prevalent reinforcement learning~(RL) methods for fine-tuning LLM reasoners, such as GRPO or Leave-one-out PPO, abandon the learned value function in favor of empirically estimated returns. This hinders test-time compute scaling that relies on using the value-function for verification. Yet if parallel test-time compute is already part of the deployment plan, training should be designed to support it. In this work, we propose RL that augments any ``value-free'' RL method by jointly training the LLM as both a reasoner and a generative verifier using RL-generated data, adding verification capabilities without significant overhead. Empirically, RL boosts MATH accuracy by over 20\% with parallel sampling and enables efficient test-time compute scaling compared to the base RL method. RL also exhibits strong generalization capabilities for both easy-to-hard and out-of-domain tasks. Furthermore, RL achieves higher performance when jointly scaling parallel and sequential test-time compute with a long reasoning R1 model. More broadly, RL instantiates the principle of co-training for test-time scaling: jointly optimizing for task performance and a capability useful at inference, using data that RL training already produces.