OPO: Making Decision-Focused Data Acquisition Decisions

Egon Per\v{s}ak; Miguel F. Anjos

REVIEW 3 major objections 5 minor 15 references

OPO: Making Decision-Focused Data Acquisition Decisions

T0 review · 3 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read The paper claims that data acquisition decisions should be optimised for the downstream decisions they enable, and that OPO, a fully differentiable optimise-predict-optimise model with a learnable linear surrogate for acquisition value…

desk verdict A useful and mostly sound extension of decision-focused learning to data acquisition, but the experiments need a proxy-objective baseline before the central claim is supported. read the letter →

arxiv 2504.15062 v1 pith:PEPW3SYC submitted 2025-04-21 math.OC cs.AI

Egon Peršak , Miguel F. Anjos This is my paper · ORCID

classification math.OCcs.AI MSC 90C2790C1590C3568T07

keywords decision-focusedlearningdataacquisitiondifferentiableoptimizationcontextualstochasticsurrogatelinearobjectiveorienteeringproblemmaskedinputpredictionshortestpath

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

OPO makes a simple but underused claim: the point of collecting data is to make better downstream decisions, so the data acquisition problem itself should be optimised for decision quality. The paper models acquisition as a constrained binary choice, replaces the unknown value of each acquisition plan with a learnable linear surrogate $\langle \pi, s\rangle$, and trains the whole pipeline—acquisition, masked prediction, and downstream optimisation—end-to-end by differentiating through two optimisation layers. On a drone reconnaissance task where a limited-range drone chooses which tiles of an aerial image to photograph before a shortest-path problem is solved, the learned acquisition strategy outperforms random search and fixed heuristics, with relative regret falling from 0.469 to 0.240 after tuning. If correct, this gives a general recipe for aligning costly data collection with what a decision-maker actually cares about.

What carries the argument

The machinery is a surrogate linear objective parameterised by vector $\pi$ over binary acquisition decisions $s$, constrained by known constraints $A(s) \le 0$; solving it gives $s^*(\pi)$. Around this, the paper builds a fully differentiable chain: a masked tokenization layer $I(z,s;\Lambda)=\operatorname{diag}(s)t(z)+(1-s)\otimes \Lambda$ replaces unobserved image segments with a learnable mask token $\Lambda$, a masked-input vision transformer predicts travel costs, and a shortest-path solver produces the decision. Two non-sequential differentiable-optimisation layers carry gradients: blackbox differentiation through the acquisition solver and a perturbed Fenchel-Young loss through the downstream shortest path. The counterfactual gradient $\partial I/\partial s$ is what connects a change in acquisition choice to a change in prediction, and it is what requires the Full Observation Assumption.

What would settle it

Run the OPO training loop on a dataset that is only partially observed, so that ground-truth context for unobserved variables is not available, and check whether the gradient computation can be replaced or the method reverts to random-search performance; if it cannot, the Full Observation Assumption is load-bearing. Separately, construct a data acquisition problem whose optimal solution lies in the interior of the convex hull of the feasible acquisition set; if the linear surrogate $\langle \pi, s\rangle$ cannot recover that optimum, the paper's boundary assumption fails.

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Extended reading notes

Core claim

The central claim is that data acquisition decisions can be treated as part of an optimise-predict-optimise chain and learned end-to-end, rather than fixed by coverage heuristics. Concretely, the paper posits an unknown value function $p(s)$ over binary acquisition decisions, and proposes to approximate its optimal solution by maximising a linear surrogate $\langle \pi, s\rangle$ subject to known acquisition constraints; $\pi$ is then learned so that the entire system minimises downstream decision loss. On the drone reconnaissance problem, the best configuration combines warm-starting the surrogate parameter $\pi$ from a random search, then fine-tuning the prediction model and $\pi$ together with the decision loss, which the paper reports as the first decision-focused model for data acquisition. The experiments show the learned acquisition strategy beats random search and fixed strategies in downstream objective value, with the best tuned model reducing relative regret by about 17% compared with the best non-learned strategy.

Load-bearing premise

The training set must contain fully observed contextual vectors and true parameters for every example, because the counterfactual gradient in Eq. (10) needs to say how the prediction would have changed if different data had been acquired; if the training labels are themselves only partially observed, the OPO loop cannot run.

Editorial extensions

If this is right

If OPO is correct, any constrained data acquisition problem with a differentiable downstream predictor can in principle be aligned with decision quality, not just with coverage or prediction error.
Warm-starting $\pi$ via cheap random search and then fine-tuning end-to-end is a practical recipe that outperforms training from scratch or fixing the acquisition strategy.
The learned $\pi$ values carry meaning as relative values of acquiring each piece of context, which could be used to rank data sources before a full acquisition budget is fixed.
PFL and DFL objectives give different behaviour under learned acquisition, so choosing the training loss must be guided by the downstream task structure, not by convention.
The experimental protocol gives a concrete benchmark: on Warcraft shortest path with orienteering constraints, a learned DA strategy reaches relative regret 0.240, a number future methods can be compared against.

Reading between the lines

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

An extension the paper leaves open is reading $\pi$ as a shadow price: if the acquisition budget is relaxed, the learned score could rank which additional sensors or tiles to buy, though the paper only frames $\pi$ as relative value within a fixed budget.
Because OPO treats acquisition as constrained token selection, the same architecture could plausibly be adapted to language tasks where deciding which tokens or documents to read before answering is itself the acquisition decision, an extension the authors only conjecture.
The observed sensitivity of $\pi$ optimisation to the learning rate points to a testable improvement: schedule the $\pi$ learning rate dynamically after fine-tuning begins to stabilise the two-level optimisation.
The main scaling bottleneck is the two heuristic solver calls per batch; replacing the combinatorial acquisition layer with a solver-free differentiable surrogate would let OPO scale to larger orienteering-style problems, a direction the paper explicitly identifies as needed.

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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

Colleague — quick take: OPO is a real extension, not a repackaging. It treats data acquisition as a trainable optimise-predict-optimise loop, replaces proxy coverage objectives with a learned linear surrogate on the acquisition variables, and differentiates through a masked tokenizer and a downstream solver. The masked-input differentiable tokenization (diag(s) t(z) + (1-s)⊗Λ) is a neat piece of engineering, and having two non-sequential implicit layers is genuinely new as far as I know. The authors are also honest about their assumptions: Section 2.1 admits the convex-hull boundary condition is an assumption, and Assumption 3.1 states the full-observation requirement up front. Code is linked and the math is coherent. Credit where due.

Soft spots. The stress-test note is right: there is no coverage or mutual-information baseline. The paper motivates OPO by saying DA is usually solved for proxies like coverage, then only compares against random search over pi and fixed-pi. So the empirical claim 'decision-focused DA beats what people actually do' is unsupported. Random search is a useful control, but it is not the incumbent heuristic. That should be fixable in a revision. Second, the headline 17% relative-regret improvement is selected via best-of-N validation init and learning-rate tuning on the best validation init (Tables 1-2). Not fraudulent, but the reported advantage is optimistic. Third, the linear surrogate justification is representational rather than constructive: any binary feasible point is an extreme point of the convex hull, so a linear objective can in principle encode any optimal strategy, but that does not tell you gradient descent will find that pi or that the surrogate will transfer. Minor: 'first decision-focused model for data acquisition' and 'first instance of non-sequential optimisation layers' are strong claims; the first depends on literature coverage that is thinner than I'd like, and the second is a novelty claim best softened.

Bottom line: the method is sensible and the architecture is a genuine contribution. The missing baseline is a real gap but not a fatal one; the assumptions are stated and the mechanism is sound enough to deserve referee time. I'd send this out with a request for a proxy-baseline comparison, a less cherry-picked number, and toned-down claims.

Referee Report

3 major / 5 minor

Summary. The paper proposes OPO (optimise-predict-optimise), a differentiable pipeline for making constrained data-acquisition decisions in contextual stochastic optimization. A binary acquisition vector s is chosen by solving a linear surrogate max ⟨π,s⟩ subject to A(s)≤0; the selected contextual variables are passed through a masked ViT that predicts the uncertain coefficients θ; the downstream optimization problem is solved; and a PFL or DFL loss is backpropagated through the two optimization layers. The experiments concern a drone-reconnaissance variant of the Warcraft shortest-path problem, where an orienteering constraint limits the number of visited tiles. Ablations vary fixed vs. learned π, pretrained vs. fine-tuned vs. jointly trained predictors, and PFL vs. DFL losses, and the paper reports that warm-starting plus fine-tuning with a learned π gives the best results, with a claimed 17% relative-regret improvement over the best fixed-π baseline.

Significance. The idea of optimizing data-acquisition decisions against downstream decision loss is natural and potentially useful, and the paper's decomposition into a linear surrogate, a masked predictor, and a differentiable solver is clean. Strengths include a clear statement of the full-observation assumption, released code, and a sensible ablation design. The linear-surrogate justification is actually stronger than the paper claims: every binary feasible solution is an extreme point of its convex hull, so a linear objective can represent any optimal deterministic DA strategy. The main weaknesses are empirical: no coverage or mutual-information baseline is tested, and the headline relative-regret numbers are not transparently defined. If those are fixed, the paper would be a solid contribution to decision-focused learning and data acquisition.

major comments (3)

[Sec. 4.3, Tables 1–2] The central quantitative claim, a 17% relative-regret reduction from 0.289 to 0.240, is not verifiable from the paper. 'Relative regret' is never defined, and the values 0.469, 0.289, 0.260, and 0.240 do not appear in any table. The table columns labeled lossDFL contain values around 38–43 while the perfect-information objective is 29.64, suggesting that the tables report absolute objective values rather than the regret defined in Eq. (7). Please define the metric, state the selection protocol, and report both the raw objective and the regret so the claim can be checked.
[Secs. 1, 4.3, 5] The paper motivates OPO by arguing that DA is typically solved by proxy objectives such as coverage or mutual information, but the experiments include no such baseline. Random search over π is an uninformative control, not a proxy-objective heuristic. Therefore the paper does not demonstrate its claimed advantage over existing heuristics, only over random search. I recommend adding at least a coverage-oriented orienteering baseline (e.g., reward proportional to geographic spread or a hand-crafted visiting pattern) and, if possible, a mutual-information or informative-path-planning baseline to the drone task.
[Assumption 3.1, Eq. (10)] The Full Observation Assumption is load-bearing because the counterfactual gradient in Eq. (10) requires fully observed z and θ to compute ∂I/∂s. When historical data are themselves only partially observed, the proposed training loop cannot be applied. This assumption narrows the practical scope of the paper considerably, and the text should either discuss relaxations or explicitly restrict the claims to the full-observation setting.

minor comments (5)

[Sec. 2.1] Since the feasible solutions are binary, every feasible s is an extreme point of the convex hull of the feasible set; the boundary-condition justification for the linear surrogate is therefore automatically satisfied and should be stated as a fact rather than as a belief.
[Table 1 caption] The relationship between the MIN and BEST columns is unclear; for example, in the PFL-training lossDFL FIXED-FT row BEST (39.66) is worse than MIN (37.40) under a minimization objective. Explain how the best initialization is selected and why BEST can exceed the minimum.
[Sec. 4.2, Table 2] The π learning rate is tuned on the best-performing validation initialization only, so the improvement in Table 2 may confound initialization choice with learning-rate choice; report the sweep over multiple initializations or explicitly acknowledge this in the limitations.
[Eq. (10)] The notation ∂I/∂s followed by a vector of token gradients is dimensionally ambiguous; define the Jacobian explicitly.
[Throughout] The manuscript contains unfinished formatting artifacts ('Draft A PREPRINT', an unresolved 'available here' link for the code) and a few grammatical slips; these should be corrected before resubmission.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: OPO's surrogate objective is learned from data, not defined in terms of its own output, and the derivation is self-contained.

full rationale

The paper's derivation chain is not circular. Equation (1) defines the true data acquisition problem via an unknown function p(s), and Equation (2) proposes a linear surrogate <pi, s> parameterized by pi. This surrogate is not defined in terms of the paper's output; pi is a learnable parameter optimized by gradient descent on the downstream DFL or PFL loss (Equation (9)). Thus the model does not fit a parameter to a target and then rename that fit as a prediction. The convex-hull boundary condition used to justify the linear surrogate is an explicit modeling assumption, not a circular reduction. Assumption 3.1 (Full Observation Assumption) is an independence premise required for the counterfactual gradient in Equation (10); it assumes access to fully observed training data, not the validity of the OPO result. The differentiable optimization layers are taken from Pogančić et al. (2020), Berthet et al. (2020), and SurCo (Ferber et al., 2023) as external machinery; these are independent implementation tools, and the paper explicitly notes that OPO can be interpreted as applying SurCo to an implicit objective, which is an acknowledgment rather than a hidden self-citation. The only self-citation (Peršak & Anjos, 2024) appears in a related-work remark and is not load-bearing. The lack of a coverage or mutual-information proxy baseline is an experimental design and correctness concern, not a circularity: comparing against random search and fixed-pi baselines may under-support the claim of superiority over proxy heuristics, but it does not make any derivation reduce to its own inputs. Therefore the paper warrants a circularity score of 0.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central contribution rests on the learned surrogate reward pi and on domain assumptions covering full observation, known constraints, and linear downstream objectives. No new physical or mathematical entities are introduced, and no quantities are fitted that are then relabelled as predictions.

free parameters (2)

Surrogate reward vector pi = Learned; best learning rate 7e-4 in experiments
Linear objective coefficients in Eq. (2); fitted by gradient descent on the downstream loss. The paper's central mechanism and the source of the learned DA strategy.
Mask token Lambda = Learned vector of size d_m=32
Imputation vector in Eq. (3) and part of the prediction model parameters; a standard learnable imputation parameter, not an ad hoc device.

assumptions (5)

domain assumption Assumption 3.1 (Full Observation Assumption): training set consists of fully observed z and theta
Required for the counterfactual gradient in Eq. (10); if training data is partially observed the gradient computation fails.
ad hoc to paper Linear surrogate validity: p(s) can be replaced by <pi, s> without losing the optimal solution
Section 2.1 asserts the optimal solution lies on the boundary of the convex hull of the feasible set, without proof.
domain assumption Data acquisition constraints A(s) are known a priori and solver-amenable
Section 2.1 assumes constraints are known and can be handled by a solver; the method does not learn constraints.
domain assumption Contextual decision task has a linear objective and certain constraints
Eq. (5) assumes uncertainty only in the objective parameters theta, not in constraints or functional form.
standard math Prediction model and optimization layers are differentiable
The gradient chain in Eq. (9) requires differentiable prediction and DO layers such as Pogančić et al. (2020) and PFYL.

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Cite this review

Pith. "Pith review of OPO: Making Decision-Focused Data Acquisition Decisions." pith.science (2026). https://pith.science/paper/PEPW3SYC

@misc{pith2026250415062,
  author       = {Pith},
  title        = {Pith review of: OPO: Making Decision-Focused Data Acquisition Decisions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PEPW3SYC}},
  note         = {Machine review of arXiv:2504.15062}
}

read the original abstract

We propose a model for making data acquisition decisions for variables in contextual stochastic optimisation problems. Data acquisition decisions are typically treated as separate and fixed. We explore problem settings in which the acquisition of contextual variables is costly and consequently constrained. The data acquisition problem is often solved heuristically for proxy objectives such as coverage. The more intuitive objective is the downstream decision quality as a result of data acquisition decisions. The whole pipeline can be characterised as an optimise-then-predict-then-optimise (OPO) problem. Analogously, much recent research has focused on how to integrate prediction and optimisation (PO) in the form of decision-focused learning. We propose leveraging differentiable optimisation to extend the integration to data acquisition. We solve the data acquisition problem with well-defined constraints by learning a surrogate linear objective function. We demonstrate an application of this model on a shortest path problem for which we first have to set a drone reconnaissance strategy to capture image segments serving as inputs to a model that predicts travel costs. We ablate the problem with a number of training modalities and demonstrate that the differentiable optimisation approach outperforms random search strategies.

Figures

Figures reproduced from arXiv: 2504.15062 by the authors.

**Figure 1.** OPO stages for a single instance on the Drone Reconnaissance For Shortest Path experiment from a [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗

**Figure 2.** Distribution of mean validation set results for the random search strategy. We note the best performing [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.

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" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION format.date year duplicate empty "emp...

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Ferber, A. M., Huang, T., Zha, D., Schubert, M., Steiner, B., Dilkina, B., and Tian, Y. Surco: Learning linear surrogates for combinatorial nonlinear optimization problems. In International Conference on Machine Learning, pp.\ 10034--10052. PMLR, 2023

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Johnson-Yu, S., Finocchiaro, J., Wang, K., Vorobeychik, Y., Sinha, A., Taneja, A., and Tambe, M. Characterizing and improving the robustness of predict-then-optimize frameworks. In International Conference on Decision and Game Theory for Security, pp.\ 133--152. Springer, 2023 a

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Modeling robustness in decision-focused learning as a stackelberg game

Johnson-Yu, S., Wang, K., Finocchiaro, J., Taneja, A., and Tambe, M. Modeling robustness in decision-focused learning as a stackelberg game. In Proceedings of the 2023 International Conference on Autonomous Agents and Multiagent Systems, pp.\ 2908--2909, 2023 b

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