Targeting-Aware Acquisition Function

• The topic is a specialized acquisition strategy that directly scores queries based on their expected impact on the ultimate decision objective.
• It integrates active learning, Bayesian optimization, and experimental design by replacing generic proxies with task-specific metrics such as validation accuracy and uncertainty reduction.
• It employs advanced mathematical formulations, ranking methods, and multi-level optimization to overcome the limitations of traditional heuristic-based approaches.

Searching arXiv for recent and relevant papers on targeting-aware acquisition functions and closely related formulations. A targeting-aware acquisition function is an acquisition rule whose score is aligned with the actual downstream target of a sequential decision problem rather than with a generic proxy alone. In the recent literature, that target has taken multiple forms: validation accuracy after retraining in active learning, validation/generalization performance in bilevel Bayesian optimization, reduction of posterior uncertainty over scientific parameters in experimental design, boundary identification for treatment assignment under aggregate and differentially private queries, localization of a source as the maximizer of a field, and the improvement of a user-specified goal functional $J(\theta)$ through data acquisition (Ding et al., 2023, Bao et al., 22 May 2025, Dunbar et al., 2022, Shchetkina, 7 Jul 2025, González-Gudiño et al., 16 Oct 2025, Yao et al., 23 Feb 2026). The unifying principle is explicit task alignment: acquisition is designed to optimize what the procedure ultimately cares about, while still handling exploration, uncertainty, feasibility, and computational constraints.

1. Conceptual basis

In active learning and Bayesian optimization, classical acquisition rules frequently optimize surrogate criteria such as predictive uncertainty, diversity, expected improvement, or confidence bounds. Several recent works treat this as insufficient when the true objective is validation performance, parameter identification, or a task-specific notion of success. RAMBO formulates active learning as direct utility maximization over validation accuracy, with

$$U(S; H_t) = \mathrm{Acc}(M_{\phi^*(S,H_t)}; V), \qquad \phi^*(S,H_t) = \arg\min_{\phi} L_{\mathrm{train}}(M_\phi; D_t \cup S),$$

so the selected batch is the one predicted to maximize post-training validation accuracy rather than uncertainty alone (Ding et al., 2023). In bilevel BO for fine-tuning RoBERTa-base, the same principle appears as an outer loop that is optimized with respect to a validation metric while the inner loop minimizes training loss (Bao et al., 22 May 2025).

This alignment principle also appears outside conventional active learning. In privacy-constrained targeting, the acquisition is designed for the policy boundary $f(x)-c=0$ rather than for pointwise maximization, because the relevant decision is whether treatment effect exceeds treatment cost (Shchetkina, 7 Jul 2025). In climate-model experimental design, candidate region–time windows are scored by the posterior covariance they would leave over uncertain GCM parameters, so acquisition is defined by uncertainty reduction about parameters rather than by predictive fit at the queried location (Dunbar et al., 2022). In goal-oriented influence maximization, the target is an explicit user goal $\mathcal{G}(\theta)$, such as test loss, predictive entropy, or the value of an optimizer-recommended design (Yao et al., 23 Feb 2026).

A recurrent contrast is with fixed heuristics chosen a priori. Deep active learning with adaptive acquisition argues that no single heuristic consistently dominates and instead learns a policy from reinforcement feedback collected during labeling rounds (Haussmann et al., 2019). Inverse Bayesian optimization reaches a similar conclusion in a different setting: standard PI, EI, and UCB do not fully explain human sequential search, and augmented thresholded acquisitions better capture the strategy of “explore enough to learn the target direction” (Sandholtz et al., 2021). This suggests that “targeting-aware” denotes a family of acquisition designs rather than a single formula.

2. Mathematical formulations

The central mathematical move is to encode the task target directly into the acquisition. The resulting forms differ by problem class, but they share a common structure: a score for a candidate query, batch, region, or action is defined in terms of its expected effect on the true objective.

Setting	Targeted quantity	Representative acquisition
Active learning (Ding et al., 2023)	Validation accuracy after retraining	$U(S;H_t)=\mathrm{Acc}(M_{\phi^*(S,H_t)};V)$
Bilevel BO for LLM fine-tuning (Bao et al., 22 May 2025)	Validation metric with training-loss awareness	$$a_{\mathrm{mix}}(x)=\alpha EI_{\mathrm{val}}(x)-(1-\alpha)LCB_{\mathrm{train}}(x)$$
Privacy-preserving targeting (Shchetkina, 7 Jul 2025)	Boundary refinement around $f(x)-c=0$	$TAAF(R)=\beta V(R)-|m(R)-c|$
Climate experimental design (Dunbar et al., 2022)	Parametric uncertainty reduction	$$U(W_k)=\big(\det \mathrm{Cov}(\theta\mid W_k y)\big)^{-1}$$
Goal-oriented influence acquisition (Yao et al., 23 Feb 2026)	Improvement in user-specified goal $J(\theta)$	$$U(S; H_t) = \mathrm{Acc}(M_{\phi^*(S,H_t)}; V), \qquad \phi^*(S,H_t) = \arg\min_{\phi} L_{\mathrm{train}}(M_\phi; D_t \cup S),$$0

In RAMBO, the acquisition is not trained to regress absolute utility values; instead, it is trained as a ranking model over candidate batches using a RankNet objective. For utility samples $$U(S; H_t) = \mathrm{Acc}(M_{\phi^*(S,H_t)}; V), \qquad \phi^*(S,H_t) = \arg\min_{\phi} L_{\mathrm{train}}(M_\phi; D_t \cup S),$$1 with utilities $$U(S; H_t) = \mathrm{Acc}(M_{\phi^*(S,H_t)}; V), \qquad \phi^*(S,H_t) = \arg\min_{\phi} L_{\mathrm{train}}(M_\phi; D_t \cup S),$$2 and $$U(S; H_t) = \mathrm{Acc}(M_{\phi^*(S,H_t)}; V), \qquad \phi^*(S,H_t) = \arg\min_{\phi} L_{\mathrm{train}}(M_\phi; D_t \cup S),$$3,

$$U(S; H_t) = \mathrm{Acc}(M_{\phi^*(S,H_t)}; V), \qquad \phi^*(S,H_t) = \arg\min_{\phi} L_{\mathrm{train}}(M_\phi; D_t \cup S),$$4

$$U(S; H_t) = \mathrm{Acc}(M_{\phi^*(S,H_t)}; V), \qquad \phi^*(S,H_t) = \arg\min_{\phi} L_{\mathrm{train}}(M_\phi; D_t \cup S),$$5

with $$U(S; H_t) = \mathrm{Acc}(M_{\phi^*(S,H_t)}; V), \qquad \phi^*(S,H_t) = \arg\min_{\phi} L_{\mathrm{train}}(M_\phi; D_t \cup S),$$6 if $$U(S; H_t) = \mathrm{Acc}(M_{\phi^*(S,H_t)}; V), \qquad \phi^*(S,H_t) = \arg\min_{\phi} L_{\mathrm{train}}(M_\phi; D_t \cup S),$$7 and $$U(S; H_t) = \mathrm{Acc}(M_{\phi^*(S,H_t)}; V), \qquad \phi^*(S,H_t) = \arg\min_{\phi} L_{\mathrm{train}}(M_\phi; D_t \cup S),$$8 otherwise (Ding et al., 2023). This converts task targeting into a learned pairwise utility ordering.

In bilevel BO for LLM fine-tuning, the target-aware structure is explicit in the bilevel problem

$$U(S; H_t) = \mathrm{Acc}(M_{\phi^*(S,H_t)}; V), \qquad \phi^*(S,H_t) = \arg\min_{\phi} L_{\mathrm{train}}(M_\phi; D_t \cup S),$$9

with separate GP surrogates for $f(x)-c=0$0 and $f(x)-c=0$1. The paper studies mixed outer acquisitions such as

$f(x)-c=0$2

and reports that the best empirical configuration uses EI in the inner loop and UCB in the outer loop (Bao et al., 22 May 2025).

In privacy-preserving targeting, the target is the treatment boundary rather than the global maximum. The regional acquisition is

$f(x)-c=0$3

where $f(x)-c=0$4 and $f(x)-c=0$5 are the posterior predictive mean and variance of the regional average, and $f(x)-c=0$6 is treatment cost (Shchetkina, 7 Jul 2025). High variance supports exploration, while small $f(x)-c=0$7 emphasizes regions near the policy boundary.

A further generalization appears in curvature-aware Expected Free Energy, where a Gaussian preference distribution $f(x)-c=0$8 encodes the desired target outcome $f(x)-c=0$9. The acquisition is

$\mathcal{G}(\theta)$0

so targeting and information gain appear in a single functional (Meera et al., 27 Mar 2026).

3. Design patterns and optimization strategies

A common design pattern is multi-level optimization. RAMBO uses a bilevel framework in which the inner level fits the surrogate on shorter utility samples and the outer level optimizes hyperparameters so that the surrogate generalizes to longer histories: $\mathcal{G}(\theta)$1

$\mathcal{G}(\theta)$2

with

$\mathcal{G}(\theta)$3

This makes targeting aware of the growing history $\mathcal{G}(\theta)$4, since longer sets act as validation tasks for the acquisition surrogate (Ding et al., 2023).

Another recurring pattern is auxiliary alignment to the target distribution. RAMBO adds an OT-distance head that predicts $\mathcal{G}(\theta)$5, regularizing candidate selection toward the validation distribution (Ding et al., 2023). Bilevel BO with SWA uses separate surrogates for validation metric and training loss, allowing exploration strength to adapt to the observed sensitivity between them (Bao et al., 22 May 2025). In privacy-preserving targeting, posterior uncertainty already incorporates differentially private noise through $\mathcal{G}(\theta)$6, so boundary-focused acquisition automatically reflects privacy-induced measurement degradation (Shchetkina, 7 Jul 2025).

Several works also integrate targeting into the surrogate itself rather than only into the acquisition layer. Approximation-aware BO replaces global posterior fidelity with utility-calibrated variational inference: $\mathcal{G}(\theta)$7 The variational approximation is therefore optimized jointly with the decision utility, which reallocates approximation capacity toward decision-relevant regions (Maus et al., 2024). This differs materially from the usual pattern of first fitting an approximate GP globally and only then maximizing an acquisition.

Targeting can also be embedded into path planning or stateful policies. In jammer localization, UCB over the surrogate field,

$\mathcal{G}(\theta)$8

is treated as targeting-aware because the task is to locate the maximizer of the field. The path planner then incorporates acquisition into edge costs,

$\mathcal{G}(\theta)$9

so the agent moves through high-acquisition regions while obeying mobility constraints (González-Gudiño et al., 16 Oct 2025).

4. Representative instantiations across domains

In active learning, targeting-aware acquisition is most explicit when the selected batch is ranked by its predicted effect on validation accuracy. RAMBO combines a set-based encoder, pairwise ranking, OT regularization, and bilevel generalization across growing histories. Its decision rule is

$U(S;H_t)=\mathrm{Acc}(M_{\phi^*(S,H_t)};V)$0

after candidate generation through a margin filter and batching (Ding et al., 2023). A different active-learning instantiation is reinforcement-learned acquisition. There the state is a product Gaussian over predictive moments on a bootstrap shortlist, and the policy is trained with rewards combining marginal-likelihood improvement and label diversity: $U(S;H_t)=\mathrm{Acc}(M_{\phi^*(S,H_t)};V)$1 with $U(S;H_t)=\mathrm{Acc}(M_{\phi^*(S,H_t)};V)$2 (Haussmann et al., 2019).

In hyperparameter optimization for language-model fine-tuning, targeting-aware acquisition separates the training objective from the real deployment objective. The inner loop minimizes training loss using early stopping and SWA, while the outer acquisition targets validation performance. The paper evaluates EI-only, UCB-only, UCB-EI, and EI-UCB; the targeting-aware interpretation is that the outer decision rule should reflect the true target metric even when training loss and validation behave differently (Bao et al., 22 May 2025).

In privacy-preserving personalization, the acquisition acts on regions rather than points because the platform exposes only aggregate, noisy queries. The latent CATE surface $U(S;H_t)=\mathrm{Acc}(M_{\phi^*(S,H_t)};V)$3 is updated through integral GP operators, and the acquisition chooses the next region $U(S;H_t)=\mathrm{Acc}(M_{\phi^*(S,H_t)};V)$4 to refine treatment decisions near the boundary $U(S;H_t)=\mathrm{Acc}(M_{\phi^*(S,H_t)};V)$5 (Shchetkina, 7 Jul 2025). This is a structurally different use of acquisition from classical BO, but it preserves the core idea of goal alignment.

In scientific experimental design, the target is posterior contraction in parameter space. For uncertain GCM parameters, candidate latitudes and seasonal windows are scored by a D-optimal criterion,

$U(S;H_t)=\mathrm{Acc}(M_{\phi^*(S,H_t)};V)$6

which functions as a proxy for expected information gain about $U(S;H_t)=\mathrm{Acc}(M_{\phi^*(S,H_t)};V)$7 (Dunbar et al., 2022). The acquisition therefore ranks prospective measurements by how much they would reduce uncertainty in the calibrated parameters, not by local predictive variance alone.

Behavioral and human-in-the-loop settings yield yet another variant. In inverse BO for sequential target search, standard PI, EI, and UCB are augmented with angular thresholds $U(S;H_t)=\mathrm{Acc}(M_{\phi^*(S,H_t)};V)$8 or $U(S;H_t)=\mathrm{Acc}(M_{\phi^*(S,H_t)};V)$9 so that insufficient exploration is penalized: $$a_{\mathrm{mix}}(x)=\alpha EI_{\mathrm{val}}(x)-(1-\alpha)LCB_{\mathrm{train}}(x)$$0 The augmentation operationalizes the strategy of enforcing enough angular deviation to learn target direction (Sandholtz et al., 2021).

A more abstract formulation is GOIMDA, where the acquisition is the expected first-order influence of a new labeled example on a user-specified goal: $$a_{\mathrm{mix}}(x)=\alpha EI_{\mathrm{val}}(x)-(1-\alpha)LCB_{\mathrm{train}}(x)$$1

$$a_{\mathrm{mix}}(x)=\alpha EI_{\mathrm{val}}(x)-(1-\alpha)LCB_{\mathrm{train}}(x)$$2

This makes “targeting-aware” literal: the acquisition is parameterized by the chosen goal functional $$a_{\mathrm{mix}}(x)=\alpha EI_{\mathrm{val}}(x)-(1-\alpha)LCB_{\mathrm{train}}(x)$$3 (Yao et al., 23 Feb 2026).

5. Empirical behavior and computational trade-offs

Empirical results repeatedly show that explicit targeting can outperform proxy-driven acquisition, particularly when the proxy is unstable or misaligned. In RAMBO, full RAMBO on CIFAR-10 ablation with $$a_{\mathrm{mix}}(x)=\alpha EI_{\mathrm{val}}(x)-(1-\alpha)LCB_{\mathrm{train}}(x)$$4 and $$a_{\mathrm{mix}}(x)=\alpha EI_{\mathrm{val}}(x)-(1-\alpha)LCB_{\mathrm{train}}(x)$$5 reaches $$a_{\mathrm{mix}}(x)=\alpha EI_{\mathrm{val}}(x)-(1-\alpha)LCB_{\mathrm{train}}(x)$$6, whereas weaker variants are reported around $$a_{\mathrm{mix}}(x)=\alpha EI_{\mathrm{val}}(x)-(1-\alpha)LCB_{\mathrm{train}}(x)$$7–$$a_{\mathrm{mix}}(x)=\alpha EI_{\mathrm{val}}(x)-(1-\alpha)LCB_{\mathrm{train}}(x)$$8; the method also reports total runtimes of approximately $$a_{\mathrm{mix}}(x)=\alpha EI_{\mathrm{val}}(x)-(1-\alpha)LCB_{\mathrm{train}}(x)$$9h$f(x)-c=0$0m on CIFAR-10 and $f(x)-c=0$1h on SVHN on a single GPU without parallelism (Ding et al., 2023). In bilevel BO-SWA on GLUE with RoBERTa-base, EI-UCB achieves average score $f(x)-c=0$2, compared with $f(x)-c=0$3 for standard fine-tuning, corresponding to an improvement of up to $f(x)-c=0$4 (Bao et al., 22 May 2025).

The same pattern appears in privacy-preserving targeting. Under the Criteo AI Labs uplift setting, uniform querying can achieve as little as $f(x)-c=0$5 of the non-privacy-preserving targeting potential in the $f(x)-c=0$6-query, $f(x)-c=0$7 condition, whereas the strategic querying method based on TAAF reaches $f(x)-c=0$8–$f(x)-c=0$9 across the reported privacy settings and is statistically indistinguishable from Causal Forest (Shchetkina, 7 Jul 2025). In human-search inverse BO, augmented thresholded acquisitions improve total out-of-sample log-likelihood from $TAAF(R)=\beta V(R)-|m(R)-c|$0 for standard acquisitions to $TAAF(R)=\beta V(R)-|m(R)-c|$1 for symmetric thresholding and $TAAF(R)=\beta V(R)-|m(R)-c|$2 for asymmetric thresholding (Sandholtz et al., 2021).

Targeting-aware acquisitions also change where exploration occurs. In climate design, the largest information gain typically, but not always, results from regions near the ITCZ; in the stationary single-latitude setting, utility peaks near the subtropical precipitation minima at $TAAF(R)=\beta V(R)-|m(R)-c|$3, while wider stencils move the optimum closer to the ITCZ (Dunbar et al., 2022). In active jammer localization, acquisition-aware path planning reduces localization error relative to uninformed baselines: for example, in Chicago Downtown, A-UCB* with $TAAF(R)=\beta V(R)-|m(R)-c|$4 reports SME $TAAF(R)=\beta V(R)-|m(R)-c|$5 and BOE $TAAF(R)=\beta V(R)-|m(R)-c|$6, compared with RIS SME $TAAF(R)=\beta V(R)-|m(R)-c|$7 and BOE $TAAF(R)=\beta V(R)-|m(R)-c|$8 (González-Gudiño et al., 16 Oct 2025).

The computational cost of targeting-awareness is usually shifted from label acquisition or function evaluation toward surrogate training, posterior updating, or meta-optimization. RAMBO reduces full retraining cost through interpolation-based utility labels (Ding et al., 2023). Bilevel BO-SWA pays for separate surrogates and nested evaluation loops (Bao et al., 22 May 2025). Integral GP updates under aggregate queries require regional kernel computations and $TAAF(R)=\beta V(R)-|m(R)-c|$9 linear algebra, though moderate query budgets remain tractable (Shchetkina, 7 Jul 2025). Utility-calibrated SVGPs add an expected log-utility term but remain scalable through minibatching and inducing variables (Maus et al., 2024). GOIMDA avoids explicit posterior inference, but it replaces it with inverse-Hessian–vector products computed by CG or LiSSA (Yao et al., 23 Feb 2026).

6. Limitations, misconceptions, and directions

A common misconception is that targeting-aware acquisition is merely exploitation under a different name. The surveyed methods do not support that view. Boundary-focused TAAF includes an explicit variance term $$U(W_k)=\big(\det \mathrm{Cov}(\theta\mid W_k y)\big)^{-1}$$0 (Shchetkina, 7 Jul 2025); curvature-aware EFE contains both a risk term and an information-gain term (Meera et al., 27 Mar 2026); climate design uses posterior uncertainty reduction (Dunbar et al., 2022); and EI-UCB places UCB, not EI, in the outer validation-targeting loop precisely to preserve exploration in generalization space (Bao et al., 22 May 2025). The distinction is not exploration versus exploitation, but whether either is organized around the true downstream target.

Another misconception is that targeting-awareness removes the need for auxiliary heuristics. In practice, many methods retain them. RAMBO still uses a margin filter to generate candidate batches before scoring them with the learned surrogate (Ding et al., 2023). Reinforcement-learned active acquisition bootstraps from entropy ranking and only learns to warp the top of that ranking (Haussmann et al., 2019). Jammer localization first maximizes UCB over the feasible grid and then embeds acquisition in path costs (González-Gudiño et al., 16 Oct 2025). This indicates that targeting-aware acquisition is often layered on top of simpler candidate-generation machinery.

The principal limitations are computational and modeling-related. Severe history shift, new classes, or label noise may require re-pretraining in learned active learning (Ding et al., 2023). GP assumptions, sensitivity estimation, and budget overhead limit bilevel BO-SWA (Bao et al., 22 May 2025). Very strong differential privacy noise or extremely small lengthscale degrades aggregate-query targeting (Shchetkina, 7 Jul 2025). In climate design, sparse designs and short averaging windows can induce multimodality and reduce reliability of the predicted utility map (Dunbar et al., 2022). GOIMDA depends on stable inverse-curvature estimates, while curvature-aware EFE becomes more difficult in high-dimensional spaces where Hessian information is expensive or noisy (Yao et al., 23 Feb 2026, Meera et al., 27 Mar 2026).

Several papers make the extension space explicit. The BO-SWA work lists multi-objective BO, constrained BO, dynamic acquisition switching, and better uncertainty modeling as natural extensions (Bao et al., 22 May 2025). Privacy-constrained targeting points to adaptive region refinement and nonstationary kernels under high-dimensional heterogeneity (Shchetkina, 7 Jul 2025). Goal-oriented influence acquisition notes that diversity-aware batching is a natural next step for sequential designs (Yao et al., 23 Feb 2026). Taken together, these results suggest that targeting-aware acquisition functions are evolving toward more explicit goal specification, stronger coupling between surrogate learning and decision utility, and broader treatment of constraints, distribution shift, and path-dependent costs.