WIST: Web-Grounded Iterative Self-Play Tree for Domain-Targeted Reasoning Improvement

Recent progress in reinforcement learning with verifiable rewards (RLVR) offers a practical path to self-improvement of language models, but existing methods face a key trade-off: endogenous self-play can drift over iterations, while corpus-grounded approaches rely on curated data environments. We present WIST, a Web-grounded Iterative Self-play Tree framework for domain-targeted reasoning improvement that learns directly from the open web without requiring any pre-arranged domain corpus. WIST incrementally expands a domain tree for exploration, and retrieves and cleans path-consistent web corpus to construct a controllable training environment. It then performs Challenger--Solver self-play with verifiable rewards, and feeds learnability signals back to update node posteriors and guide subsequent exploration through an adaptive curriculum. Across four backbones, WIST consistently improves over the base models and typically outperforms both purely endogenous self-evolution and corpus-grounded self-play baselines, with the Overall gains reaching +9.8 (Qwen3-4B-Base) and +9.7 (OctoThinker-8B). WIST is also domain-steerable, improving Qwen3-8B-Base by +14.79 in medicine and Qwen3-4B-Base by +5.28 on PhyBench. Ablations further confirm the importance of WIST's key components for stable open-web learning. Our Code is available at https://github.com/lfy-123/WIST.