J4R: Learning to Judge with Equivalent Initial State Group Relative Policy Optimization

To keep pace with the increasing velocity of large language models (LLM) development, model output evaluation has transitioned away from time-consuming human evaluation to automatic evaluation, where LLMs themselves are tasked with assessing and critiquing other model outputs.LLM-as-judge models are a class of generative evaluators that excel in evaluating relatively simple domains, like chat quality, but struggle in reasoning intensive domains where model responses contain more substantive and challenging content.To remedy existing judge shortcomings, we explore training judges with reinforcement learning (RL).We make three key contributions: (1) We propose the Equivalent Initial State Group Relative Policy Optimization (EIS-GRPO) algorithm, which allows us to train our judge to be robust to positional biases that arise in more complex evaluation settings.(2) We introduce ReasoningJudgeBench, a benchmark that evaluates judges in diverse reasoning settings not covered by prior work.(3) We train Judge for Reasoning (J4R), a 7B judge trained with EIS-GRPO that outperforms GPT-4o and the next best small judge by 6.7% and 9%, matching or exceeding the performance of larger GRPOtrained judges on both JudgeBench and Rea-soningJudgeBench.