On-Policy Delta Distillation for Multilingual Math Reasoning

On-Policy Distillation (OPD) is emerging as a promising alternative to reinforcement learning for LLM post-training, yet its effectiveness in multilingual settings remains underexplored. We study OPD and its advanced variant, On-Policy Delta Distillation (OPD2), for mathematical reasoning in English, Korean, and Japanese. OPD2 improves OPD by using the probability gap between a post-trained teacher and its base model as the learning signal. Experiments with Qwen3 show that OPD2 consistently outperforms the original OPD, with particularly strong improvements in Korean and Japanese, and generally narrows the English-Korean performance gap. We further find that English-only OPD can also increase performance for Korean and Japanese, but often shifts the responses toward English, highlighting the importance of multilingual data to preserving target-language responses.