Efficient On-Policy Distillation for Language Models: A Survey of Costs, Trade-Offs, and Evaluation

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On-policy distillation (OPD) transfers teacher behavior through feedback on student-generated trajectories. Its efficiency is often expressed in incompatible units: fewer examples, shorter rollouts, lower memory, higher throughput, or cheaper deployment. These gains need not coincide, and an inexpensive update need not minimize the cost of reaching a target capability. We survey efficient OPD through six connected tracks: data, rollout, teacher supervision, optimization, systems, and deployment amortization. A common accounting framework separates additive resource expenditure from elapsed time and peak memory, while preserving differences in state distributions, teacher access, and learning objectives. We accompany the synthesis with a versioned evidence ledger that records the workload, denominator, measurement boundary, and quality condition behind reported efficiency results. The resulting audit exposes several sources of non-comparability, including changed sequence caps, omitted preparation, stage-local memory statistics, and increased scoring cost hidden by faster generation. Building on existing general and formula-driven OPD surveys, our contribution is an operational organization of efficiency evidence and a reproducible cost-to-quality evaluation protocol. We conclude with testable research questions about budget allocation, state coverage, supervision value, and amortized deployment. The literature cutoff is October 25, 2026; no new model-training experiments are claimed.