Goal-Oriented Influence-Maximizing Data Acquisition for Learning and Optimization

Active data acquisition is central to many learning and optimization tasks with deep neural networks, yet remains challenging because most approaches rely on predictive uncer- tainty estimates that are difficult to obtain reliably. To this end, we propose Goal-Oriented Influence-Maximizing Data Acquisition (GOIMDA), an active acquisition algorithm that by- passes explicit uncertainty estimation. GOIMDA selects inputs by maximizing their expected influence on a user-specified goal functional, such as test loss, predictive entropy, or the value of an optimizer-recommended design. Leveraging first-order influence functions, we derive a tractable acquisition rule that combines the goal gradient, training-loss curvature, and candidate sensitivity to model parameters. We show theoretically that, for generalized linear models, GOIMDA approximates predictive-entropy minimization up to a correction term accounting for goal alignment and prediction bias, thereby implicitly capturing uncer- tainty without maintaining a Bayesian posterior. Empirically, across learning tasks (including image and text classification) and optimization tasks (including noisy global optimization benchmarks and neural-network hyperparameter tuning), GOIMDA consistently reaches target performance with substantially fewer labeled samples or function evaluations than uncertainty-based active learning and Gaussian-process Bayesian optimization baselines.