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

Reinforcement learning with verifiable rewards (RLVR) provides reliable outcome supervision for language model reasoning, but scalar trajectory rewards offer limited guidance for token-level credit assignment. Existing self-distillation methods incorporate privileged teacher information through fixed strategies: direct distribution matching may destabilize successful behavior, while magnitude modulation provides limited corrective guidance after failure. We propose Hybrid Hindsight Self-Distillation (H$^2$SD), which adapts both teacher context and update strategy to trajectory correctness. For successful trajectories, the teacher conditions on the verified student response and a rephrasing instruction to rescore the original tokens. These scores modulate reward-derived updates while preserving advantage signs. For failed trajectories, a verified reference hint guides corrective supervision through reverse KL distillation. Across Sudoku, Calcudoku, Arrow Maze, and mathematical reasoning with two Qwen3 models, H$^2$SD achieves an overall average accuracy of 43.33%, outperforming the strongest baseline by 11.43 percentage points while maintaining stable optimization.

Recent advances in large language model (LLM) reasoning through reinforcement learning rely on annotated datasets for verifiable rewards, which may limit models' ability to surpass human-level performance. While self-play offers a promising alternative, prior methods yield only marginal or even negative gains on post-trained models because they generate problems that cluster around familiar concepts rather than discovering novel ones. We introduce Open-Ended Self-Improving Reasoner (OpenSIR), a self-play framework in which a single LLM alternates teacher and student roles to generate and solve novel problems without external verifiers or annotated data. Starting from a single seed problem, OpenSIR sustains open-ended exploration through diversity rewards that push the model toward unfamiliar concepts and difficulty calibration that keeps problems learnable. Across seven math benchmarks, OpenSIR consistently improves all models, averaging +3.6 points on instruction models and +3.1 on reasoning models, while recent self-play baselines yield marginal or even negative gains; starting from a single trivial seed, it also surpasses GRPO baselines trained on over 7K annotated examples. Despite training only on self-generated math, OpenSIR is the only self-play method that transfers to general reasoning, improving by at least +4.4 points on reasoning models.

Self-play fine-tuning enables large language models to improve beyond supervised fine-tuning without additional human annotations by contrasting annotated responses with self-generated ones. Many existing methods rely on a fixed divergence regime. SPIN is closely related to a KL-based regime, SPACE to a Jensen-Shannon-style objective via noise contrastive estimation, and SPIF to $χ^2$-regularized self-play. Since these divergences exhibit different strengths depending on the distributional gap between model and target, no single choice appears to provide favorable learning dynamics across training stages. We propose IRIS (Interpolative Rényi Iterative Self-play), a Rényi-based self-play fine-tuning framework with a continuously adjustable objective. IRIS decomposes into two independent tilted risk terms over annotated and synthetic data, with exponential importance weights controlled by the order parameter $α$. We show that several self-play objectives can be interpreted as limiting or representative regimes at particular values of $α$, providing a unified theoretical perspective on these methods. An adaptive order schedule further adjusts $α$ to the distributional gap, shifting from sharper importance weighting early in training to smoother refinement near convergence. Theoretically, we establish the fixed-point property of IRIS and analyze how $α$ controls gradient concentration. Experiments on Zephyr-7B and Qwen2.5-3B across ten benchmarks show that IRIS improves upon baselines, reaching 44.57% average score with gains across iterations. In our setting, IRIS with only 26$k$ annotated samples surpasses standard supervised fine-tuning trained on the full 200$k$ dataset.