Large-scale prediction models using tools from artificial intelligence (AI) or machine learning (ML) are increasingly common across a variety of industries and scientific domains. Despite their effectiveness, training AI and ML tools at scale can cost tens or hundreds of thousands of dollars (or more); and even after a model is trained, substantial resources must be invested to keep models up-to-date. This paper presents a decision-theoretic framework for deciding when to refit an AI/ML model when the goal is to perform unbiased statistical inference using partially AI/ML-generated data. Drawing on portfolio optimization theory, we treat the decision of {\it recalibrating} a model or statistical inference versus {\it refitting} the model as a choice between ``investing'' in one of two ``assets.'' One asset, recalibrating the model based on another model, is quick and relatively inexpensive but bears uncertainty from sampling and may not be robust to model drift. The other asset, {\it refitting} the model, is costly but removes the drift concern (though not statistical uncertainty from sampling). We present a framework for balancing these two potential investments while preserving statistical validity. We evaluate the framework using simulation and data on electricity usage and predicting flu trends.