Abstract This study assesses whether a hybrid prediction–optimisation workflow can be used as an exploratory exercise for Brazilian federal budget allocation under severe data constraints. Using executed expenditure by budgetary function (2000–2023; N = 24), a multi-output XGBoost model is estimated to link spending profiles to GDP growth, inflation, and the Gini index; Bayesian optimisation (Tree-structured Parzen Estimator/Optuna) is then applied to search, within explicit bounds and penalties, for allocation vectors that maximise a stated objective function favouring higher growth and lower inflation and inequality. To mitigate data scarcity, the short series is augmented with 1048 synthetic observations generated through controlled noise injection, bootstrapped resampling and variational autoencoder reconstruction. Under randomised K-fold cross-validation on the augmented dataset, the model achieves mean R 2 = 0.97 and mean MSE = 0.04, while diagnostics indicate larger errors at extreme values and a persistent training–validation gap. A secondary robustness check uses an anti-leakage design by applying cross-validation to the 24 real observations and generating synthetic data only within each training fold. This yields markedly weaker generalisation for GDP growth and inflation (overall mean MSE = 1.03; overall mean R 2 = −0.45), with positive performance remaining only for the Gini index ( R 2 = 0.60). Under these conditions, the optimisation step identifies a scenario that satisfies the objective function on standardised outputs (GDP growth = 1.15; inflation = −0.04; Gini = −0.17). The results support the use of the workflow to compare scenarios under explicit assumptions, rather than to produce prescriptive budget guidance.
Nonato et al. (Thu,) studied this question.