The paper compares two dominant post-training methods for reasoning LLMs: (RLVR) and (OPD). Prior work combines them within a single step, either by weighted addition or teacher-modulated rescaling. The authors test a simple alternative: apply OPD first, then RLVR in sequence.
Across logic and math reasoning benchmarks, the sequential OPD-then-RL scheme consistently beats pure OPD, pure RLVR, and all joint optimization baselines, with up to a 26.7 pass@1 margin on logic tasks. Analysis reveals why: OPD expands the student’s coverage of teacher-supported solutions, and RL then sharpens within that support, while joint optimization causes the two signals to interfere.
This is interesting because it provides a practical recipe for combining two complementary techniques without the complexity of joint training. The authors also find that the OPD validation score reliably indicates when to switch to RL, and that OPD is a better cold start for RL than standard supervised fine-tuning.