Offline reinforcement learning and off-policy evaluation evaluates dynamic treatment rules based on retrospectively collected data prior to deployment. In recent AI applications, state and reward information is recorded as complex text or image, which recent AI advancements such as LLM-as-a-judge can label with unknown bias. Expert annotation may be available but at a higher cost. For example, safety classification via cheap but imperfect classifiers vs. expensive expert review. We show how a limited budget for ground-truth data-annotation can be used via doubly-robust OPE with missing rewards, and we optimize variance-optimal annotation probabilities for sequential off-policy evaluation, where the target policy value is estimated from annotated data. We characterize the optimal annotation probabilities for sequential forward-monotone annotation protocols, and provide a feasible batch-adaptive implementation. Our work is motivated by a collaboration with a homelessness services nonprofit that writes casenotes for individuals over time. Our method can be used to unlock trustworthy inference from casenote data and answer new inferential questions such as: how does expanding outreach effort over time affect progress towards a housing application and improvement in housing placement? In simulations and on two real datasets - casenotes from the nonprofit and human-preference votes from LMArena - we see reductions in RMSE of 34-65% for housing placement and 17-68% for progress towards a housing application at budgets of 40% of full annotation and above, and by 55-62% at every budget on LMArena.

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