Robust Bayesian Decision Making under Adversarial Uncertainty

Haripriya Harikumar; Sammie Katt; Samuel Kaski; Yasir Zubayr Barlas

REVIEW 3 major objections 5 minor 39 references

Robust Bayesian Decision Making under Adversarial Uncertainty

T0 review · 3 major / 5 minor · reviewed 2026-07-14 · grok-4.5

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Conventional decision-aware design can lock onto high-confidence but fragile decisions; targeting information about the worst-case robust optimum yields more stable choices under adversarial variation.

desk verdict Clean, usable extension of DEIG to min-over-ε-ball robust decisions; experiments prove the matched threat model well, not the abstract’s broader “hidden effects” claim. read the letter →

arxiv 2607.08590 v2 pith:Y5DJ33OI submitted 2026-07-09 cs.LG

Haripriya Harikumar , Sammie Katt , Yasir Zubayr Barlas , Samuel Kaski This is my paper · ORCID

classification cs.LG

keywords Bayesianexperimentaldesignactivelearningdecision-awareacquisitionadversarialrobustnessrobustdecisionmakingexpectedinformationgainStackelberggameosteoarthritis

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Scientific experiments are often run to support decisions, not merely to learn parameters. Existing decision-aware design methods select data that quickly reduce uncertainty about the nominally best action, yet they ignore how that action can reverse under small unmodeled shifts in certain variables. This paper formalizes an adversarially robust optimal decision as the action that maximises worst-case utility inside a user-specified ball of perturbations, then derives an acquisition criterion (AR-DEIG) that reduces entropy over the posterior of that robust optimum. On synthetic regressions and an osteoarthritis dataset, ordinary decision-EIG becomes overconfident in brittle choices, while the robust criterion produces decisions whose quality holds under the same perturbations. Anyone who designs sequential experiments for medicine or other high-stakes settings should care, because the method aligns data collection with decision stability rather than nominal optimality.

What carries the argument

AR-DEIG (Adversarially Robust Decision Expected Information Gain): the acquisition rule that selects the next query by maximising the expected reduction in entropy of the posterior over the robust-optimal decision d*(ξt,ξa;ε)=argmax_d min_{ξ'a∈Aε(ξa)} Ud(ξt,ξ'a). It redefines the quantity of interest from nominal optimality to decision stability under worst-case perturbation inside the ε-ball.

What would settle it

On a held-out test set whose true adversarial variables or true perturbation magnitudes differ from those used during acquisition, check whether AR-DEIG still improves worst-case and CVaR decision quality over ordinary DEIG; if it does not, or if performance collapses once the evaluation ball leaves the design ball, the central claim fails.

Watch

Extended reading notes

Core claim

Sequential experimental design should acquire data to reduce uncertainty about the adversarially robust optimal decision rather than the nominal optimum. For a design split into ordinary and adversarial coordinates, the robust decision under budget ε is the action maximising the minimum utility over the closed ball of adversarial perturbations. Conventional decision-aware criteria can converge rapidly to high-confidence yet fragile decisions; the AR-DEIG criterion—expected information gain about the posterior over that robust optimum—yields decisions that remain significantly more stable under adversarial variation of the designated variables.

Load-bearing premise

The decision-maker can correctly name the adversarial variables and choose a fixed perturbation radius that actually covers the relevant real-world failure modes; if the true threats lie outside that ball or in unnamed coordinates, the robust target is misspecified.

Editorial extensions

If this is right

Decision-aware active learning that ignores adversarial coordinates can produce overconfident, brittle policies that degrade under modest input shifts.
Explicitly optimising information about the worst-case decision improves mean, worst-case and CVaR performance on both synthetic and real scientific data.
The same framework recovers ordinary DEIG in the limit as the perturbation radius ε goes to zero.
Larger ε produces more conservative decisions, which can become overly pessimistic and degrade performance if the budget is misspecified.
Domain experts who can name the adversarial variables and a plausible ε can use the criterion without changing the underlying Bayesian predictive model.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The same worst-case-over-ball construction can be dropped into other information criteria simply by redefining the quantity of interest as the robust argmax.
If adversarial variables must be discovered rather than named by experts, an outer sensitivity loop that ranks coordinates by decision-flip frequency would be a natural extension.
Because the criterion only needs predictive samples under perturbed inputs, it can wrap any black-box Bayesian model without altering the likelihood.
In sequential medical settings the method implies early queries should deliberately probe regions where treatment rankings reverse under realistic covariate noise.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

This is a controlled, honest extension of Filstroff et al.’s DEIG: replace the nominal optimal-decision random variable with the worst-case value over an ε-ball on known adversarial coordinates, then take ordinary EIG on the posterior over that robust decision (AR-DEIG, Eq. 12). Lemma 3.1 correctly recovers DEIG as ε o0; Props 1–2 are elementary set-inclusion facts. That is the real novelty—nothing more, nothing less.

What they do well: the acquisition function is cleanly defined, code is linked, and the synthetic GP suite (1-D and higher-D, smooth vs rough Matérn outcomes) plus OAI BMI-as-adversary experiments show clear gains on mean/worst-case/CVaR10 and lower decision-flip rates versus RS/US/PEIG/TEIG/DEIG under the same ball used for acquisition. Cross-ε plots and the large-ε degradation (Fig. 18) behave as the theory predicts. Runtime table is transparent about the cost. For anyone already working in decision-aware BOED or personalized-medicine active learning who can name the adversarial coordinates and pick a plausible ε, this is immediately usable.

Soft spot, in proportion: the abstract and intro language about “hidden or weakly modeled effects” overreaches. All robustness metrics sample the identical A_ε ball (or same directions) that defines the target. The paper itself states the decision-maker must identify ξ_a and ε; if the true failure modes sit outside that ball or in unidentified variables, both d* and the queries are misspecified. That is a genuine limitation of the evaluation protocol, not a math error, and it is the main reason the broader reliability claim is not yet settled. Free parameters (ε, GP kernels, ridge λ) are standard for the setting.

Who it is for: Bayesian experimental design and decision-aware AL people who already accept known adversarial coordinates. It deserves a serious referee; the contribution is real inside its stated model. I would bring it to reading group and would cite the AR-DEIG criterion when I need a robust decision target. Send it out.

Referee Report

3 major / 5 minor

Summary. The paper studies sequential decision-aware experimental design under adversarial uncertainty. It defines a robust decision value V_d(ξ_t, ξ_a; ε) = min_{ξ'_a ∈ A_ε(ξ_a)} U_d(ξ_t, ξ'_a) with A_ε the Euclidean ball of radius ε around known adversarial coordinates, takes the robust-optimal decision d* = argmax_d V_d, and proposes AR-DEIG as expected information gain about the posterior mass on that discrete robust decision (Eqs. 9–12). Propositions 1–2 and Lemma 3.1 follow immediately from set inclusion and the ε o 0 limit. Experiments on 1-D/higher-D synthetic GPs and the OAI osteoarthritis dataset compare AR-DEIG to RS, US, PEIG, TEIG and DEIG, reporting mean/worst-case/CVaR10 under the same ball, decision-flip rates, and recovery of a robust ground-truth decision.

Significance. The work cleanly connects targeted decision-aware active learning (Filstroff et al.) with a min-max robust utility, supplies a principled EIG criterion, elementary but correct supporting propositions, public code, and consistent empirical gains (including lower flip rates) under a correctly specified ball threat model. If domain experts can name the adversarial coordinates and a budget ε, the method is practically useful. The contribution is incremental rather than foundational; its broader claim of reliability under truly hidden or weakly modeled effects is not yet established by the matched train/eval experiments.

major comments (3)

[Abstract and §3] Abstract and §3: The abstract claims that AR-DEIG yields decisions that are “significantly more stable and reliable under adversarial variation” and against “hidden or weakly modeled effects.” All reported robustness metrics (Figs. 2–3, 7–9; mean/worst-case/CVaR10) and the robust ground-truth used in Figs. 7–8 are obtained by sampling the identical closed ball A_ε that defines V_d and the AR-DEIG target (Eqs. 9–12). Cross-ε (Fig. 4) and large-ε degradation (Fig. 18) remain inside the same family of balls. The experiments therefore establish only that EIG about a correctly specified robust decision improves performance under that model; they do not test unidentified variables, effects outside A_ε, or misspecified ε. Either the abstract language must be aligned with the evaluated threat model or misspecification experiments must be added.
[§3] §3 (definitions of ξ = (ξ_t, ξ_a), A_ε and U_d = y_d): The framework assumes the decision-maker can identify the adversarial coordinates and a fixed ε such that the relevant worst-case effects lie inside the Euclidean ball, with latent utility set equal to the predictive outcome. The paper notes domain-expert identification but supplies no sensitivity analysis when ξ_a is misspecified, when the true perturbation is non-ball (sparse, distributional, or coupled), or when ε is badly chosen (the degradation at ε = 20 in Fig. 18 already shows over-conservatism). This assumption is load-bearing for the claim of reliability under real-world adversarial variation.
[§4, Appendix A/B] §4 and Appendix A/B: Computation of the inner min that defines V_d is left unspecified for continuous GPs. In 1-D a grid or dense sampling is feasible; in higher dimensions (20-D experiment, multi-dimensional adversarial subspace in Figs. 7–8) the quality of the min approximation directly affects both the acquisition target and the reported robust ground-truth. Runtime (Table 1) already shows AR-DEIG 1.7–2.4 imes slower than DEIG; without a clear, scalable procedure for the min (and its interaction with the MC/Gauss–Hermite outer expectation) the practicality and reproducibility of the method remain incomplete.

minor comments (5)

[§2–§3] Notation for the design is overloaded: ξ is used both for the full design and for the controllable part; the split (ξ_t, ξ_a) appears only in §3. A consistent notation table would help.
[§4] Figs. 2–3, 7–9 captions are long and partially repeat the main text; the green-curve emphasis is helpful but the confidence bands are hard to read in some panels.
[§3] Lemma 3.1 is essentially immediate from the definitions; it could be stated as a remark rather than a numbered lemma.
[§5] Related-work discussion of distributionally robust BO and adversarially robust GPs is present but could more sharply contrast the decision-uncertainty target of AR-DEIG with function-level robust optimization.
[throughout] Minor typos and spacing issues appear throughout (e.g., “BA YESIAN”, “EV ALUA TION”, missing spaces around some equations).

Circularity Check

1 steps flagged · score 1.0 of 10

No significant circularity in the derivation; AR-DEIG is ordinary EIG re-targeted at the posterior over a worst-case decision defined by min over an explicit ball, with propositions following by set inclusion and a trivial limit lemma.

self citation load bearing [Section 3 (after Eq. 8) and Related Work 5.1]
"Our formulation is closely related to the targeted active learning framework of Filstroff et al. [2024], which connects utility modeling with downstream decision-making. We redefine the target of information as a robust decision random variable. ... Targeted active learning [Filstroff et al., 2024] introduces a decision-aware Expected Information Gain (EIG) criterion..."

The non-robust DEIG baseline and the overall decision-as-quantity-of-interest framing are imported from a prior paper sharing senior author Kaski. This is ordinary incremental self-citation rather than a load-bearing uniqueness theorem or an unverified premise that forces the robust claims; the AR-DEIG equations and propositions stand independently once the robust target is defined. Score contribution is therefore only 1.

full rationale

The paper's central construction (Section 3) defines the robust value Vd(ξt,ξa;ε)=min_{ξ'a∈Aε(ξa)} Ud(ξt,ξ'a), the robust decision d*=argmax Vd, the posterior masses πrob_d=P(d=d*|D), and then AR-DEIG as the ordinary expected entropy reduction of that discrete random variable (Eq. 12). This is definitional re-targeting of the DEIG criterion of Filstroff et al. (2024), not a quantity forced by a fitted constant or by self-reference. Proposition 1 and 2 are immediate consequences of the definition of min over nested sets Aε1⊆Aε2; Lemma 3.1 is the elementary limit Aε→{ξa} as ε→0. No parameter is fitted to data and then re-presented as a prediction; the acquisition function itself contains no free parameters beyond the user-chosen ε and the identified coordinates ξa. Self-citation of the DEIG line (and related Kaski-group decision-aware EIG papers) is present and supplies the non-robust baseline, but is not load-bearing for the robust extension: the worst-case utility, the Stackelberg interpretation, and the AR-DEIG formula are written out and proved from first principles inside the manuscript. Empirical claims (mean/worst-case/CVaR, flip rates, recovery of robust ground truth) are experimental comparisons under a matched threat model, not tautological rewrites of the acquisition objective. Hence the derivation chain is self-contained; the only minor circularity-adjacent element is ordinary self-citation of the non-robust precursor, which does not force the robust result.

Assumptions & free parameters 3 free parameters · 5 assumptions · 3 invented entities

The central claim rests on standard Bayesian decision theory plus an explicit adversarial-ball model of unmodeled effects. The main free knob is the user-chosen ε (and which coordinates are adversarial). No new physical entity is postulated; the invented objects are the robust value Vd, the robust decision random variable Drob_best, and the AR-DEIG criterion. Background EIG identities and GP predictive models are taken from prior literature.

free parameters (3)

adversarial radius ε = experiment-specific values e.g. 0.1, 0.3, 0.5, 0.7, 20.0
User-specified budget defining Aε(ξa); acquisition and evaluation performance depend strongly on this choice (cross-ε plots Fig. 4; degradation at large ε, Prop. 2 and Fig. 18).
GP kernel hyperparameters (lengthscales, ν, variance, noise) = e.g. ℓsmooth=0.6, ν=5/2 vs ℓrough=0.18, ν=1/2; SE variance/lengthscale sampling rules in §4.3.1
Synthetic data and models use Matérn/SE kernels with fixed or sampled lengthscales and variances that shape smoothness of decision curves and thus which decisions look robust.
ridge regularization λ in OAI linear outcome model
Appendix linear model uses ridge least squares; λ is a free regularization choice affecting estimated decision-dependent outcomes.

assumptions (5)

standard math Bayesian decision theory: optimal decision maximizes expected utility under the posterior (Berger 2013).
Used as the foundation for both nominal and robust decision definitions in §2.2 and §3.
domain assumption Worst-case effects of unmodeled factors are adequately represented by min over an ℓ-norm ball of radius ε around known adversarial coordinates ξa.
Section 3 defines Aε and the Stackelberg/min-max robust decision; the whole acquisition target depends on this threat model.
domain assumption Latent utility of a decision equals the predictive outcome Ud=yd from the outcome model.
Stated explicitly in §3; collapses utility modeling to outcome prediction.
domain assumption Domain experts can identify which variables are adversarial and set a realistic ε.
Section 3: 'we assume that the decision-maker is able to identify these variables'; method is agnostic to identification procedure but requires it.
standard math As ε→0, Aε collapses to {ξa} so AR-DEIG reduces to DEIG.
Lemma 3.1; continuity of the construction with prior decision-aware EIG.

invented entities (3)

Robust decision value Vd(ξt,ξa;ε)=min_{ξ'a∈Aε} Ud(ξt,ξ'a) and robust-optimal decision d*
purpose: Replace nominal utility with worst-case utility so the decision target is stable under adversarial shifts.
Defined in Eq. 9–10; not a physical entity but a new decision-theoretic object for this paper.
Drob_best(ξ̃;ε) and posterior masses πrob_d
purpose: Quantity of interest whose entropy reduction defines the acquisition objective.
Eq. 11; robust analogue of Filstroff et al. Dbest.
AR-DEIG acquisition criterion
purpose: Select pool points that maximize expected information gain about the robust-optimal decision posterior.
Eq. 12; the paper's main methodological contribution.

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Cite this review

Pith. "Pith review of Robust Bayesian Decision Making under Adversarial Uncertainty." pith.science (2026). https://pith.science/paper/Y5DJ33OI

@misc{pith2026260708590,
  author       = {Pith},
  title        = {Pith review of: Robust Bayesian Decision Making under Adversarial Uncertainty},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Y5DJ33OI}},
  note         = {Machine review of arXiv:2607.08590}
}

read the original abstract

Scientific experiments are often designed to maximize information gain, yet in many applications the primary objective is to support reliable downstream decision-making. Existing decision-aware experimental design and active learning methods typically assume well-specified outcome models and implicitly rely on the stability of the optimal decision under real-world perturbations. In practice, however, experimental outcomes are frequently influenced by hidden or weakly modeled effects, which can substantially alter decision optimality and lead to misleading conclusions. We study sequential adversarially robust decision-aware experimental design, where data acquisition has to take into account information gain against plausible worst-case unexpected effects, modeled here as variation in adversarial variables. Building on Bayesian decision theory, we formalize an adversarially robust optimal decision under this setting and derive a principled Bayesian experimental design criterion. The criterion explicitly targets decision stability rather than nominal optimality. Experiments on synthetic and real-world scientific datasets show that conventional decision-aware design can converge rapidly to high confidence yet fragile decisions, while our robustness-aware approach yields decisions that are significantly more stable and reliable under adversarial variation.

Figures

Figures reproduced from arXiv: 2607.08590 by the authors.

**Figure 2.** Adversarial Robustness Evaluation: AR-DEIG achieves the strongest robustness across acquisition steps, outper [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 4.** AR-DEIG uses ϵ ∈ {0.1, 0.3, 0.5, 0.7} and is evaluated at fixed ϵeval ∈ {0.1, 0.3}. Smaller ϵ performs best under mild shifts, while intermediate values, especially 0.3 and 0.5, perform better at ϵeval = 0.3 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

Figures from the paper (35 more)

**Figure 3.** Figure 3: Adversarial Robustness Evaluation: AR-DEIG maintains superior robustness under stronger perturbations, with [PITH_FULL_IMAGE:figures/full_fig_p006_3.png]

**Figure 4.** Figure 4: Cross-ϵ robustness evaluation (ϵeval vs. ϵ) for AR-DEIG. We vary the AR-DEIG acquisition budget ϵ ∈ {0.1, 0.3, 0.5, 0.7} and evaluate the selected decisions under fixed evaluation budgets: ϵeval = 0.1 (left) and ϵeval = 0.3 (right). The x-axis shows the number of acqui…

**Figure 5.** Figure 5: Nominal Evaluation: DEIG achieves the best performance, attaining higher accuracy and significantly lower [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 6.** Figure 6: Decision flips over acquisitions: Higher flip rates [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

**Figure 7.** Figure 7: Recovery of the ground-truth robust-optimal decision versus number of acquisitions (one adversarial dimension [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

**Figure 8.** Figure 8: Recovery of the ground-truth robust-optimal decision versus number of acquisitions (three adversarial dimensions [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]

**Figure 9.** Figure 9: Adversarial Robustness Evaluation: AR-DEIG achieves consistently favorable robustness across acquisition steps, [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]

**Figure 10.** Figure 10: Three treatment plans (shown as green, orange, and blue curves) with their corresponding outcomes on the y-axis. [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]

**Figure 11.** Figure 11: ϵ = 0.5 [PITH_FULL_IMAGE:figures/full_fig_p014_11.png]

**Figure 13.** Figure 13: Adversarial Robustness Evaluation: AR-DEIG achieves the slightly better robustness across acquisition steps, [PITH_FULL_IMAGE:figures/full_fig_p014_13.png]

**Figure 14.** Figure 14: Adversarial Robustness Evaluation: AR-DEIG achieves the strongest robustness across acquisition steps, [PITH_FULL_IMAGE:figures/full_fig_p015_14.png]

**Figure 15.** Figure 15: Nominal Evaluation: DEIG achieves the best performance, attaining higher accuracy and significantly lower [PITH_FULL_IMAGE:figures/full_fig_p015_15.png]

**Figure 16.** Figure 16: Decision flips over acquisitions with ϵ = 0.1, 0.7: Higher flip rates indicate frequent reassignment of test instances to different decision curves, reflecting instability and correlating with degraded adversarial performance. ϵ = 0.5 ϵ = 0.7 (a) Accuracy ϵ = 0.5 ϵ = …

**Figure 17.** Figure 17: Nominal evaluation on the OAI dataset: (a) accuracy and (b) entropy of the posterior over decisions versus [PITH_FULL_IMAGE:figures/full_fig_p016_17.png]

**Figure 18.** Figure 18: Adversarial Robustness Evaluation: At the higher perturbation budget [PITH_FULL_IMAGE:figures/full_fig_p017_18.png]

**Figure 19.** Figure 19: Decision-EIG: Acquisition step 1 (red star indicates the query point and black vertical line is the new point the [PITH_FULL_IMAGE:figures/full_fig_p018_19.png]

**Figure 20.** Figure 20: Decision-EIG: Acquisition step 2 (red star indicates the query point and black vertical line is the new point the [PITH_FULL_IMAGE:figures/full_fig_p019_20.png]

**Figure 21.** Figure 21: Decision-EIG: Acquisition step 3 (red star indicates the query point and black vertical line is the new point the [PITH_FULL_IMAGE:figures/full_fig_p019_21.png]

**Figure 22.** Figure 22: Decision-EIG: Acquisition step 4 (red star indicates the query point and black vertical line is the new point the [PITH_FULL_IMAGE:figures/full_fig_p019_22.png]

**Figure 23.** Figure 23: Decision-EIG: Acquisition step 5 (red star indicates the query point and black vertical line is the new point the [PITH_FULL_IMAGE:figures/full_fig_p020_23.png]

**Figure 24.** Figure 24: Decision-EIG: Acquisition step 6 (red star indicates the query point and black vertical line is the new point the [PITH_FULL_IMAGE:figures/full_fig_p020_24.png]

**Figure 25.** Figure 25: Decision-EIG: Acquisition step 7 (red star indicates the query point and black vertical line is the new point the [PITH_FULL_IMAGE:figures/full_fig_p020_25.png]

**Figure 26.** Figure 26: Decision-EIG: Acquisition step 8 (red star indicates the query point and black vertical line is the new point the [PITH_FULL_IMAGE:figures/full_fig_p021_26.png]

**Figure 27.** Figure 27: Decision-EIG: Acquisition step 9 (red star indicates the query point and black vertical line is the new point the [PITH_FULL_IMAGE:figures/full_fig_p021_27.png]

**Figure 28.** Figure 28: Decision-EIG: Acquisition step 10 (red star indicates the query point and black vertical line is the new point the [PITH_FULL_IMAGE:figures/full_fig_p021_28.png]

**Figure 29.** Figure 29: AR-DEIG: Acquisition step 1 (red star indicates the query point and black vertical line is the new point the [PITH_FULL_IMAGE:figures/full_fig_p022_29.png]

**Figure 30.** Figure 30: AR-DEIG: Acquisition step 2 (red star indicates the query point and black vertical line is the new point the [PITH_FULL_IMAGE:figures/full_fig_p022_30.png]

**Figure 31.** Figure 31: AR-DEIG: Acquisition step 3 (red star indicates the query point and black vertical line is the new point the [PITH_FULL_IMAGE:figures/full_fig_p022_31.png]

**Figure 32.** Figure 32: AR-DEIG: Acquisition step 4 (red star indicates the query point and black vertical line is the new point the [PITH_FULL_IMAGE:figures/full_fig_p023_32.png]

**Figure 33.** Figure 33: AR-DEIG: Acquisition step 5 (red star indicates the query point and black vertical line is the new point the [PITH_FULL_IMAGE:figures/full_fig_p023_33.png]

**Figure 34.** Figure 34: AR-DEIG: Acquisition step 6 (red star indicates the query point and black vertical line is the new point the [PITH_FULL_IMAGE:figures/full_fig_p023_34.png]

**Figure 35.** Figure 35: AR-DEIG: Acquisition step 7 (red star indicates the query point and black vertical line is the new point the [PITH_FULL_IMAGE:figures/full_fig_p024_35.png]

**Figure 36.** Figure 36: AR-DEIG: Acquisition step 8 (red star indicates the query point and black vertical line is the new point the [PITH_FULL_IMAGE:figures/full_fig_p024_36.png]

**Figure 37.** Figure 37: AR-DEIG: Acquisition step 9 (red star indicates the query point and black vertical line is the new point the [PITH_FULL_IMAGE:figures/full_fig_p024_37.png]

**Figure 38.** Figure 38: AR-DEIG: Acquisition step 10 (red star indicates the query point and black vertical line is the new point the [PITH_FULL_IMAGE:figures/full_fig_p025_38.png]

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Pith tools

Reviewed July 14, 2026 · model on record in the stance chip above.

[1] [1]

Optimistic

Bal, Melis Ilayda and Sessa, Pier Giuseppe and Mutny, Mojmir and Krause, Andreas , booktitle=. Optimistic

[2] [2]

Adversarially

Bogunovic, Ilija and Scarlett, Jonathan and Jegelka, Stefanie and Cevher, Volkan , journal=. Adversarially

[3] [3]

Adversarial

Gloeckler, Manuel and Deistler, Michael and Macke, Jakob H , booktitle=. Adversarial

[4] [4]

Distributionally

Kirschner, Johannes and Bogunovic, Ilija and Jegelka, Stefanie and Krause, Andreas , booktitle=. Distributionally. 2020 , organization=

2020

[5] [5]

Distributionally

Husain, Hisham and Nguyen, Vu and van den Hengel, Anton , journal=. Distributionally

[6] [6]

Rainforth, Tom and Foster, Adam and Ivanova, Desi R and Bickford Smith, Freddie , journal=. Modern

[7] [7]

Amortized

Huang, Daolang and Guo, Yujia and Acerbi, Luigi and Kaski, Samuel , journal=. Amortized

[8] [8]

Bayesian

Houlsby, Neil and Husz. Bayesian. In Proceedings of the NIPS workshop on Bayesian optimization, experimental design and bandits: Theory and applications , year=