We evaluate AI agents in an online setting where tasks arrive sequentially and, before running each task, we construct an upper predictive bound on its \emph{time-to-success}---the number of interactions until the task is completed successfully. Under a limited budget, some runs are stopped early, so their time-to-success is unobserved (right-censored), and the correctness of the bound may be unknown. We introduce \emph{\textbf{PR}edictive Bounds for \textbf{O}nline \textbf{B}udget \textbf{E}fficiency} (\texttt{PROBE}), a method for constructing calibrated upper predictive bounds while adaptively allocating a limited budget across agent tasks to reduce the anticipated coverage deficit. Our method calibrates the bounds online using inverse-probability-weighted feedback together with a correction designed to minimize coverage deficit while remaining unbiased. We prove that \texttt{PROBE} provides a coverage guarantee for any finite time horizon while satisfying the budget constraint. Experiments on software engineering, retrieval-augmented generation, and instruction following show that \texttt{PROBE} attains a coverage rate closer to the target level with tighter predictive bounds than a calibrated baseline.

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