Not All Privileged Information Is Equal: What Makes OPSD Actually Work? We find that information-rich PI, such as environment observations and mistake analysis, outperforms PI that only provides ground-truth solutions. Better PI leads to better post-training performance. But can we predict which PI will work best before spending compute on post-training? We investigated three offline metrics: 🔹 Utility: A model's performance with PI can be misleading due to information leakage. 🔹 Reverse KL: Larger PI-induced distribution shifts often correlate with better post-training performance, but incorrect PI can cause equally large shifts. 🔹 Error-step KL contrast: Measuring whether PI changes the model's behavior specifically at error steps better captures its effectiveness and helps select stronger PI. What types of privileged information have you found most effective in your OPSD experiments? 📄 Paper: arxiv.org/abs/2610.22512