Recursive Self-Improvement (RSI) has gained wide attention for its ability to work with limited data. In a proposer-solver loop, a proposer model writes training tasks and a solver model learns to solve them through reinforcement learning. Such loops have succeeded in mathematics and coding, where every answer can be checked automatically. Open-ended expert tasks, like clinical report generations, have no answer key, which makes simple question-answer generation not viable. Here the proposer must also write a rubric that lists the content an answer should include and the errors it should avoid. However, the unique challenge behind model-written rubric is the comprehensiveness of it. For naively generated rubric, solvers tend to exploit it, naming the expected topics without the substance behind them, which corrupts the learning process. To solve this problem, we introduce RRI, Recursive Reward Improvement, which uses a reward hacking adversary to supervise the reward. Before the solver trains on a generated task, an adversary writes an answer that games its rubric while being as useless as possible, the same model writes an honest answer without seeing the rubric, and up to two repair steps revise the rubric to make the honest answer win. The exploits found also rewrite how future tasks and rubrics are generated. On HealthBench Professional, RRI improves the adjusted score over the Generation Only self-improvement baseline by 10.9 points at 9B and 12.4 at 27B, and by 10.3 points without any external model. In particular, the gains are largest on difficult and writing tasks. We show that the 27B model trained on the HealthBench Professional description improves by 6.6 points on PRBench Hard and 8.0 on ProfBench without seeing a task from either. We further analyze the exploitable points of model-generated question-rubric pairs to facilitate future research on open-ended self-play.

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