RiVER: Reinforcement Learning without Ground-Truth Solutions can Improve LLMs

Summary

A paper by Yingyu Lin, Qiyue Gao, and Nikki Lijing Kuang (arXiv:2606.27369) introduces RiVER, a Ranking-induced VERifiable framework for training large language models with reinforcement learning on tasks where ground-truth answers are unavailable. Standard RLVR (reinforcement learning with verifiable rewards) depends on ground-truth solutions to assign rewards, restricting its use to problems with known answers. RiVER instead targets score-based optimization tasks, using deterministic execution feedback as continuous-valued supervision in place of exact reference answers. The paper further addresses challenges that arise when applying group-relative RL to continuous-valued rewards rather than binary correctness signals. This approach extends verifiable-reward RL to domains such as optimization and engineering tasks where solutions cannot be verified against a fixed answer key, broadening the applicability of RL-based LLM post-training.