The Chase Is the Curriculum, the Capture Anchors the Credit: Pursuit-Evasion Self-Play for Zero-Data LLM Reasoning
Jing Yu, Shengchao Chen, Yiyun Tan
Abstract
Reinforcement learning with verifiable rewards has become the dominant recipe for improving large language model reasoning, yet it presumes large human-curated task collections. Zero-data self-play removes this dependency, but existing methods vet learnability only by probing candidates and rejecting post hoc, never learning where along an environment's difficulty axis to place a task, and credit the solver with sparse terminal rewards alone. We recast zero-data self-play as a pursuit-evasion game: in LURE, an LLM evader positions tasks along each environment's difficulty axis to stay one step ahead of a planner-executor pursuer that hunts it down through verifiable interaction. The evader is trained on a capture-frontier reward that peaks when the solver captures it on exactly half of its rollouts, turning barely catchable into a learned positioning strategy rather than a hand-tuned rejection band. The pursuer earns capture-anchored dense process credit, in which monotone verifier progress is group-normalized jointly with the terminal capture under a round-anchored KL that keeps the co-evolution stable. Across three verifiable reasoning environments and three backbone families, LURE outperforms advanced baselines under unified/specialist settings, while the unified model attains stronger aggregate OOD zero-shot accuracy than all trained baselines across nine held-out benchmarks from three task families.
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Classified with taxonomy v2 on Sat, 5 Sept 2026.