CritSel-OPSD: Criterion Selection for Rubric-Conditioned On-Policy Self-Distillation

Rubric-conditioned On-Policy Self-Distillation (OPSD) gives the teacher structured criteria as privileged information, but existing formulations typically expose the entire rubric throughout training. We ask whether a rubric, usually treated as an indivisible supervision object, contains redundant teacher-context information. We introduce CritSel-OPSD, a criterion-selection framework that combines leave-one-out teacher-context interventions with Top-$K$ subset construction. Selection uses trajectories from the current student and is refreshed periodically, allowing successive training blocks to use student-state-dependent contexts. Sampled Teacher Influence (STI) provides a trajectory-aligned selector. In our evaluated setting with Qwen3-8B and OpenRubrics, compact teacher contexts preserve the observed benefits of full-rubric conditioning across six diverse benchmarks while using only a subset of rubric criteria. Comparisons with random controls indicate that the central result is the viability of compact teacher-context allocation, not the universal superiority of one ranking signal. These results identify criterion selection as a design dimension distinct from rubric design and reward construction.