ARRCE: Learning Process Rubrics from Static Anchors for Open-Domain Reinforcement Learning

We introduce Asymmetrically Anchored Rubric–Response Co-Evolution ARRCE, a reinforcement learning framework that learns process rubrics from automatically synthesized static supervision for open-domain tasks. The central difficulty is to adapt evaluation criteria to the policy's changing behavior while preserving the task requirements that define a useful answer. ARRCE decouples rubric synthesis into an offline stage that constructs and freezes task and evidence-backed fact criteria, and an online stage that proposes process criteria from sampled trajectories whose relative strengths are determined by static-rubric scores. The static criteria also supervise candidate quality: a proposed process rubric is rewarded for separating held-out trajectories in a direction consistent with static performance, subject to observability and scope checks, before entering a query-specific memory for subsequent response rewards. A shared policy learns response generation and rubric proposal through separate objectives in one parameter update, yielding a synthesis loop that requires no additional human annotation of trajectory preferences or process rubrics. We instantiate this framework on dataset-derived tasks with synthesized static rubrics across healthcare, scientific question answering, and long-form writing. The experimental results show that full ARRCE improves over the response-SFT baseline by $0.057$ on ResearchQA ($+7.8\%$), $2.99$ OP points on LLMEval-Med ($+4.4\%$), $0.248$ on WritingBench ($+3.3\%$), and $0.040$ on FollowBench ($+8.1\%$), and the gains are positive across the four benchmarks.