Beyond Pass@1: Self-Play with Variational Problem Synthesis Sustains RLVR
This work addresses a bottleneck in RLVR training for LLMs on complex reasoning tasks, offering a method to sustain performance improvements across multiple benchmarks and model sizes.
The paper tackles the problem of reduced generation diversity in Reinforcement Learning with Verifiable Rewards (RLVR) for large language models, which limits Pass@k performance, by proposing a self-play strategy with variational problem synthesis that maintains policy entropy and achieves absolute gains of 18.3% and 22.8% in Pass@32 on AIME benchmarks.
Reinforcement Learning with Verifiable Rewards (RLVR) has recently emerged as a key paradigm for post-training Large Language Models (LLMs), particularly for complex reasoning tasks. However, vanilla RLVR training has been shown to improve Pass@1 performance at the expense of policy entropy, leading to reduced generation diversity and limiting the Pass@k performance, which typically represents the upper bound of LLM reasoning capability. In this paper, we systematically analyze the policy's generation diversity from the perspective of training problems and find that augmenting and updating training problems helps mitigate entropy collapse during training. Based on these observations, we propose an online Self-play with Variational problem Synthesis (SvS) strategy for RLVR training, which uses the policy's correct solutions to synthesize variational problems while ensuring their reference answers remain identical to the originals. This self-improving strategy effectively maintains policy entropy during training and substantially improves Pass@k compared with standard RLVR, sustaining prolonged improvements and achieving absolute gains of 18.3% and 22.8% in Pass@32 performance on the competition-level AIME24 and AIME25 benchmarks. Experiments on 12 reasoning benchmarks across varying model sizes from 3B to 32B consistently demonstrate the generalizability and robustness of SvS.