Certified Selective Automation of LLM Agent Evaluation

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Evaluating LLM agents still ends with a human reading trajectories, because automatic judges carry no guarantee on how often they are wrong. We ask the operational question: what fraction of agent evaluation can a judge take over, with a certificate that the error rate among auto-decided trajectories stays below a budget alpha? Agent corpora resist the standard answer: many agents attempt the same tasks, so trajectories arrive in correlated clusters, and the i.i.d. certificates of existing selective-judging methods can overstate what is safe: a naive certificate can claim 98% automation while its realized error exceeds the budget in 17.5% of task resamples. We introduce a task-level bootstrap certificate that is valid in every regime we test while matching the naive certificate's coverage; finite-sample cluster-valid alternatives certify nothing at realistic task counts. Under this certificate, a 4B logprob judge trained with SFT and reject-weighted GRPO certifies 0.30-0.59 of evaluation on tool-use and web corpora at alpha=0.1, the only judge, among strongly elicited frontier models, certifying on both headline corpora. Certified coverage is predictable before training from base rate and discrimination alone (leave-one-corpus-out R^2=0.96). Finally, the certificate doubles as a self-training filter: pseudo-labels harvested inside certified regions have contamination bounded by alpha by construction (realized 0.000-0.041 across six harvests), letting a judge enter an unseen domain at in-domain strength with zero target training labels.