Budget Allocation for Unknown Value Functions in a Lipschitz Space

Developing machine learning models often involves the evaluation of numerous intermediate models. These intermediate models arise during feature engineering, model architecture search, and hyperparam-eter tuning. For instance, during hyperparameter optimization, one might explore various configurations of learning rates, regularization parameters, and network architectures, repeatedly evaluating the model's performance at different training budgets. These accuracy assessments are influenced by the chosen model architecture and parameters, and they change as we alter these factors. Given that these evaluations are often computationally expensive, it is crucial to develop a general framework for optimally allocating resources across the vast space of potential intermediate models.