$β$-OPSD: Deriving with Policy Optimization, Training with Self-Distillation

On-policy self-distillation (OPSD) is a promising approach to improve reasoning language models, but it remains brittle in practice: making it work reliably often requires substantial engineering effort. We identify a structural source of this difficulty: vanilla OPSD is precisely the $β=1$ member of a broader policy-optimization family, where $β$ weights the KL penalty anchoring the student to a reference policy. This equivalence turns $β$ from an implicit value fixed at one into a controllable

Related evidence

These records share source-supplied organisations, an exact publisher byline, automatic topics or regions. The reason is shown on every link; related does not mean supporting, agreeing with or verifying this record.

How to cite this record

ethics.ai (30 July 2026), “$β$-OPSD: Deriving with Policy Optimization, Training with Self-Distillation,” evidence record 15252, https://ethics.ai/record/15252 (originally published by arXiv cs.LG).

Use and limitations

This page is a stable index and citation surface for a source record. ethics.ai did not author the underlying report and has not independently verified every claim. Automatic topics may be imperfect. For consequential use, quote and cite the original publisher.