LLMs can learn better coding behavior from problems with no known answers.

Many real problems do not have a gold solution waiting in a database， especially in optimization， where the best answer may be unknown， expensive， or impossible to certify.

Normal reinforcement learning works well when it can check a clear right answer， but that breaks down when the best answer is unknown.

The paper's method， called RiVER， lets the model write several programs， runs them on the same hidden tests， and rewards the programs that perform better than the others.

The key trick is that RiVER does not trust raw scores directly， because some test cases naturally produce much bigger numbers and can distort training.