SCOPE: Self-Play via Co-Evolving Policies for Open-Ended Tasks

Self-play has recently emerged as a promising paradigm for post-training Large Language Models (LLMs). In self-play, the target LLM creates the task input (e.g., a question), which it then addresses itself by producing a task output (e.g., an answer). A reward model evaluates the output, and the rewards are used to train the LLM, typically via Reinforcement Learning (RL). A key benefit of self-play for post-training LLMs is its minimal supervision costs: self-play avoids the need for high-quality input-output pairs traditionally constructed by humans or expensive proprietary models. Existing work, however, explores self-play only for verifiable tasks, such as math and coding, for which objective ground truth is available and easily checkable. In this paper, we seek to extend self-play to more realistic open-ended tasks. We propose POP, a self-play framework that uses the same LLM to synthesize evaluation rubrics along with each input-output pair. The rubric is used to evaluate outputs and train the model. Crucially, we ground the framework on a content-rich pretraining corpus to (1) enable an exploitable generation-verification gap and reduce reward hacking, and (2) prevent mode collapse. On Qwen-2.5-7B, POP increases performance of both the pretrained base model and instruction-tuned model on multiple tasks ranging from long-form healthcare QA to creative writing and instruction following.

Self-evolving LLMs excel in verifiable domains but struggle in open-ended tasks, where reliance on proxy LLM judges introduces capability bottlenecks and reward hacking. To overcome this, we introduce G-Zero, a verifier-free, co-evolutionary framework for autonomous self-improvement. Our core innovation is Hint-$δ$, an intrinsic reward that quantifies the predictive shift between a Generator model's unassisted response and its response conditioned on a self-generated hint. Using this signal, a Proposer model is trained via GRPO to continuously target the Generator's blind spots by synthesizing challenging queries and informative hints. The Generator is concurrently optimized via DPO to internalize these hint-guided improvements. Theoretically, we prove a best-iterate suboptimality guarantee for an idealized standard-DPO version of G-Zero, provided that the Proposer induces sufficient exploration coverage and the data filteration keeps pseudo-label score noise low. By deriving supervision entirely from internal distributional dynamics, G-Zero bypasses the capability ceilings of external judges, providing a scalable, robust pathway for continuous LLM self-evolution across unverifiable domains.

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.