Active data acquisition is central to many learning and optimization tasks in deep neural networks, yet remains challenging because most approaches rely on predictive uncertainty estimates that are difficult to obtain reliably. To this end, we propose Goal-Oriented Influence- Maximizing Data Acquisition (GOIMDA), an active acquisition algorithm that avoids explicit posterior inference while remaining uncertainty-aware through inverse curvature. 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, yielding uncertainty-aware behavior 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.
Figures & tables
Figure 1: GOIMDA reaches lower immediate regret with fewer acquisitions than Bayesian optimization baselines on noisy objective functions. The Bayesian optimization baselines are Gaussian Processes-based with acquisition functions: upper confidence bound (GP+UCB), expected improvement (GP+EI), probability of improvement (GP+PI), max-value entropy search (GP+MES), and knowledge gradient (GP+KG). Immediate regret is reported at each acquisition step for the Branin, Ackley, and Dropwave benchmarks under two noise levels ( σ2=0.01,0.04 ). Solid/dashed curves show the mean performance across runs, and shaded regions denote bootstrapped 95% confidence intervals of the mean (computed across runs). Across all tasks, GOIMDA consistently achieves lower regret earlier in the acquisition process, with the advantage generally becoming more pronounced at higher noise levels.
Figure 2: The parameter-bias term is crucial for effective data acquisition, and a good approximation significantly improves the acquisition performance. Using the true bias term (blue) reaches high accuracy with fewer acquisitions, and a principled approximation (orange) outperforms ignoring the bias term (dark gray dashed). The inset zoom highlights the persistent gap. Shaded regions indicate variability across runs. Test accuracy is shown versus the number of acquired labels (averaged over 200 repetitions). Higher is better.
Figure 3: GOIMDA selects the hyperparameters that provide the best prediction performance on the target test set compared to Bayesian optimization methods . The performance is evaluated in terms of the Δ test regret relative to the initial configuration (step 0) across acquisition steps. Solid line shows GOIMDA; dashed lines show Bayesian optimization baselines. Shaded regions indicate 95% bootstrap confidence intervals of the mean across 3 trials. Negative values correspond to improved target-set performance.
Acquisition Methods
% Accuracy
GOIMDA
BALD
Random
80%
88/108/116
104/109/117
138/150/173
90%
374/422/441
432/445/475
846/901/977
95%
1060/1150/1206
1514/1589/1678
4265/4522/4731
Table 1: GOIMDA requires fewer samples than BALD and random acquisition to achieve high accuracy on MNIST . The table reports 25%-, 50%-, and 75%-percentiles for the number of required data points to reach 80%, 90%, and 95% accuracy on MNIST. Higher is better.
Figure 4: GOIMDA outperforms both random acquisition and BALD on classification tasks on images of digits from MNIST (Left) and EMNIST (Middle), and the sentiment of movie reviews from the Rotten Tomatoes dataset (Right) . The test accuracy is evaluated at each acquisition step. Left: GOIMDA outperforms both random acquisition and BALD on MNIST. Middle: GOIMDA outperforms both random acquisition and BALD on EMNIST, whereas BALD only performs slightly better than random acquisition. Right: Both GOIMDA and BALD outperform the random sampling in terms of the accuracy rate at a given acquired dataset size. While GOIMDA and BALD have similar performance, GOIMDA gives slightly higher accuracy rates after the total acquisition size reaches 1,000 .
Active information gathering studies how agents choose questions, tests, or observations that reduce uncertainty and improve decisions under interaction costs.
The effectiveness of active learning hinges on the choice of the acquisition criterion by which a learning algorithm selects potentially informative data points whose label is subsequently queried. This paper proposes a novel gradient-based acquisition criterion, derived from a generalization bound introduced by Luo et al. (2022). This criterion can be applied in lieu of uncertainty measures in uncertainty sampling, or incorporated into diversity-based methods that consider the spread of sampled points in addition to the uncertainty of their labels. We provide a theoretical justification of the proposed acquisition criterion, and demonstrate its effectiveness in an empirical evaluation.
Mohamadsadegh Khosravani, Sandra Zilles
Department of Computer Science University of Regina · University of Regina
The central goal of active learning is to gather data that maximises downstream predictive performance, but popular approaches have limited flexibility in customising this data acquisition to different downstream problems and losses. We propose a rigorous loss-driven approach to Bayesian active learning that allows data acquisition to directly target the loss associated with a given decision problem. In particular, we show how any loss can be used to derive a unique objective for optimal data acquisition. Critically, we then show that any loss taking the form of a weighted Bregman divergence permits analytic computation of a central component of its corresponding objective, making the approach applicable in practice. In regression and classification experiments with a range of different losses, we find our approach reduces test losses relative to existing techniques.
Zhuoyue Huang, Freddie Bickford Smith, Tom Rainforth
In many experimental settings, active learning can improve sample efficiency by sequentially selecting where to measure, which is particularly valuable when experiments are expensive. Gaussian processes with variance-based acquisition criteria are widely used for this purpose, but have two limitations. First, they are observation-independent: their posterior variance depends only on where samples are acquired, not on what is measured, impairing their sensitivity to the structure of the acquired data. Second, they inflate the variance near boundaries, leading to excessive sampling at the edges of the space compared to the interior. These limitations undermine the gains in sampling efficiency expected from sequential acquisition. We address both limitations. We derive a reconstruction-driven design density and use the posterior mean to build a training-free warp that places more measurements where the target function varies rapidly. A geometric equalizer separately corrects boundary bias. Across sixteen synthetic and two real-data benchmarks, the geometric equalizer consistently improves function reconstruction by correcting boundary bias, while the reconstruction warp provides further gains by concentrating measurements where the posterior mean varies rapidly.
Sanna Jarl, Jens Sjölund, Jonathan J. S. Scragg +1
Department of Material Science & Engineering Uppsala University RISE · Department of Information Technology Uppsala University · RISE