arXiv:2610.38820v2 Announce Type: replace Abstract: Time-varying optimization methods often predict the locations of time-varying optima, then sample the objective function being minimized, and then compute corrections to those predictions. However, existing methods typically do not account for settings in which the number of computations is limited. Therefore, in this work we formulate a prediction-correction algorithm that is designed to obey a budget constraint on the total number of iterations it can execute over a given time horizon. We first identify a threshold on the average number of computations between samples of the objective, above which a bound from prior work certifies contraction of iterates toward a minimizer. Below this threshold, we introduce a finite-horizon contraction certificate, which we use to give budget conditions under which the tracking error admits an explicit bound that decays at a prescribed rate. We also present an algorithm to determine how many prediction and correction steps should be executed for each sample of the objective, while obeying a given budget on the allowable number of computations. Empirically, we show in a simulation that our approach reduces cumulative tracking error by 45.5 % relative to a comparable baseline approach.