Pessimistic bilevel optimization approach for decision-focused learning

Bernardo K. Pagnoncelli; Diego Jim\'enez; Hande Yaman

REVIEW 4 major objections 5 minor 29 references

Pessimistic bilevel optimization approach for decision-focused learning

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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

Pith's one-line read A pessimistic bilevel cut-generation method minimizes the true IEO loss for 0-1 combinatorial problems without surrogate losses or convex hulls.

desk verdict A real algorithmic extension for pessimistic IEO on binary DOPs, undermined by an epsilon gap in the master problem and by conclusions that overstate the experiments. read the letter →

arxiv 2501.16826 v2 pith:JTIHMTXB submitted 2025-01-28 math.OC cs.DM

Diego Jiménez , Bernardo K. Pagnoncelli , Hande Yaman This is my paper · ORCID

classification math.OCcs.DM MSC 90C1190C27

keywords contextualoptimizationdecision-focusedlearningpessimisticbilevelintegratedestimation-optimizationSPO+0-1knapsackbranch-and-cutcolumn-and-constraintgeneration

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

This paper tries to establish that the empirical risk minimization of the pessimistic integrated estimation-optimization (IEO) loss can be tackled directly for combinatorial downstream optimization problems with binary variables, without a surrogate loss or a convex-hull description. It models the learning task as a pessimistic bilevel program in which the leader chooses predictor weights and the follower, for each training sample, selects a decision that minimizes the predicted cost and maximizes the true cost, so the loss is the worst-case regret. The proposed algorithms, a column-and-constraint generation scheme and a branch-and-cut scheme, solve an $\varepsilon$-approximation of the pessimistic bilevel problem, and the branch-and-cut variant is faster and reaches optimality on tested 0-1 knapsack instances. Out-of-sample experiments on the 0-1 knapsack problem show lower regret than linear regression and SPO+ and match SPO+ when a convex hull is available, which matters because convex hulls are rarely computable for larger integer problems. If correct, this gives practitioners a direct decision-focused training procedure for combinatorial problems that previously required approximations.

What carries the argument

The central object is the pessimistic bilevel reformulation of the IEO loss: the leader minimizes the average worst-case regret over the training set, while each follower, given predicted costs $f_w(x_i)$, chooses a minimizer of the downstream problem that is worst for the true cost vector $y_i$. The mechanism that makes the problem tractable is the finite relaxation of the follower's optimality condition: since the feasible set $Z$ of a 0-1 combinatorial problem is finite, the condition that a point $z_e$ is a follower optimum is represented by an inequality on the predicted-cost gap, which the algorithm writes as an $\varepsilon$-separation constraint with a binary variable $\lambda_{ie}$. Cuts add new feasible points found by solving the subproblem, tightening the relaxation; the branch-and-cut variant adds these cuts lazily inside one master MILP, which is what makes the approach practical.

What would settle it

Take a small 0-1 knapsack instance, enumerate all feasible points, and train the method with a specific $\varepsilon$; after fitting $w$, look for a training point and feasible $z_e$ with $0 < f_w(x_i)^T(z_e - \bar z_i) < \varepsilon$. If one exists, compare the true pessimistic loss obtained by full enumeration with the loss reported by the master problem; a mismatch on any such instance shows the $\varepsilon$-approximation is not the exact pessimistic IEO loss.

Watch

Extended reading notes

Core claim

The paper's central claim is that the pessimistic IEO loss for 0-1 combinatorial optimization problems can be minimized directly, rather than through the SPO+ surrogate or through primal-dual approximations. The mathematical move is to write the empirical risk minimization as a pessimistic bilevel problem and to replace the follower's optimality condition with a finite-enumeration relaxation: because the feasible set $Z$ is finite, the statement that a point $z_e$ is a follower optimum can be expressed with binary variables and big-M constraints, and the relaxation is tightened by adding violated feasible points as cuts. The paper proves that this cut-generation procedure converges in finitely many iterations to a solution whose distance from a pessimistic optimum is at most a tolerance, and its 0-1 knapsack experiments show that the resulting predictors achieve lower out-of-sample normalized regret than linear regression and SPO+, without requiring the convex hull that SPO+ needs.

Load-bearing premise

The method assumes that a fixed positive constant $\varepsilon$ is smaller than every nonzero predicted-cost gap $f_w(x_i)^T(z_e - \bar z_i)$ that can arise, but the paper gives no rule for choosing or verifying $\varepsilon$; if some gap falls in $(0, \varepsilon)$, the reformulation treats a non-optimal point as optimal and the computed loss and predictor are not the true pessimistic IEO solution.

Editorial extensions

If this is right

For 0-1 combinatorial downstream problems, predictor fitting can target true decision regret directly, so decision-focused learning does not need a convex hull or a continuous relaxation of the feasible set.
On the tested 0-1 knapsack instances, the branch-and-cut variant is the practical solver: it reaches lower in-sample IEO loss than column-and-constraint generation within the same time limit and sometimes closes the optimality gap below $10^{-4}$.
Out of sample, the direct IEO method is competitive with or better than linear regression and SPO+: it outperforms both on more nonlinear data and matches SPO+ with convex hull when that baseline is computable.
The method inherits a meaningful overfitting risk at small sample sizes, mirroring SPO+ with convex hull, which the paper mitigates with LHS sampling and lasso regularization but does not eliminate.

Reading between the lines

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

Beyond the paper: the method's exactness claim stands on the fixed $\varepsilon$ in constraint (14c) being smaller than every nonzero predicted-cost gap, so a margin-separation check after training would either confirm or repair the claim.
Beyond the paper: the cut-generation template is not knapsack-specific; any 0-1 linear downstream problem with a finite feasible set could use the same relaxation, so the approach plausibly carries over to assignment, matching, and shortest-path decision-focused learning.
Beyond the paper: the observed small-sample overfitting suggests that direct minimization of worst-case regret amplifies noise, so a decision-aware regularizer tailored to the downstream problem, rather than generic lasso, is a natural next step.
Beyond the paper: the warm-start mechanism already used in the implementation could be developed into a hybrid training scheme that first fits a cheap surrogate such as SPO+ and then polishes with the exact pessimistic loss.

Share X Bluesky LinkedIn Reddit HN

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

You should know two things. First, the core algorithm is a genuine extension: the authors adapt Zeng's pessimistic-bilevel relaxation and column-and-constraint scheme to the case where the follower's objective depends on the leader's variables, and they add a branch-and-cut variant that clearly beats the CCG in their tests. Second, the paper's central claim does not hold as stated. It repeatedly says it minimizes the true pessimistic IEO loss without relying on approximations, but the abstract itself says "solves an \varepsilon-approximation", and the master problem (14c) hinges on an epsilon threshold with no rule for choosing it. Since w is continuous and optimized, margins can be arbitrarily small, so no fixed epsilon can separate all positive margins from zero. They even allow M = epsilon, in which case lambda = 1 forces f_w(x_i)^T(z_e - zbar_i) >= 0 and negative margins cannot be represented at all. Lemma 2 shows convergence to the epsilon-perturbed problem, not to the exact pessimistic solution. That is load-bearing, not a nit. What the paper does well: the linearization of the bilinear term is sensible, the branch-and-cut with lazy cuts is a legitimate algorithmic contribution, and the computational comparison on 0-1 knapsack is useful, including the honest reporting of overfitting at n = 100 and the SPO+(CH) comparison. The normalization of the IEO loss is a nice detail. The relaxation in Section 3.1 is clearly explained, and the proof of Lemma 1 is fine. The soft spots beyond the epsilon issue: the conclusions overstate the experiments. Tables 2 and 3 show IEO is often worse than LR or SPO+(CH), especially for delta = 1 and small n. Section 4.3 says no method consistently outperforms the others; the conclusion says IEO outperforms both LR and SPO+. The n = 500 exclusion for ny = 20 is post hoc, as the authors admit. No code or data is shipped, so the branch-and-cut details are hard to reproduce. Who is this for: researchers in decision-focused learning and contextual optimization who want a method for combinatorial DOPs without a convex hull description. It deserves a serious referee, but the referee should insist on either dropping the exact no-approximation claim or specifying how epsilon is chosen and showing that the reported results are robust to it. The n = 500 results should also be reported, or the exclusion justified as a computational limit rather than a performance filter. With those revisions the paper could be a solid contribution to the OR/MS literature.

Referee Report

4 major / 5 minor

Summary. The paper proposes a pessimistic bilevel optimization formulation for decision-focused learning in combinatorial optimization. The training problem minimizes an empirical normalized pessimistic IEO loss, where the lower level is a 0-1 linear optimization problem. The authors derive a single-level MILP using a big-M disjunction, then propose a column-and-constraint generation algorithm and a branch-and-cut algorithm, and test them on 0-1 knapsack instances against linear regression and SPO+. The central claimed contributions are exact minimization of the true pessimistic IEO loss without surrogate functions or convex hull descriptions, and superior out-of-sample performance on moderate- and large-size instances.

Significance. If the main claims were fully established, the paper would fill a genuine gap: an exact (or rigorously controlled) method for minimizing the pessimistic IEO loss for combinatorial downstream problems without a convex hull. The proposed branch-and-cut scheme is a plausible practical enhancement over column-and-constraint generation and the experiments provide useful evidence about the behavior of decision-focused training on knapsack problems. However, the exactness claim is not supported because the disjunctive reformulation uses an unspecified epsilon threshold, and the out-of-sample conclusions are contradicted by the paper's own tables. The algorithms and framework are a reasonable starting point, but the current manuscript overstates what is proven and what the experiments show.

major comments (4)

[Section 3.2, Eq. (14c)] The reformulation of the strict disjunction f_w(x_i)^T(z_e - \bar{z}_i) > 0 as f_w(x_i)^T(z_e - \bar{z}_i) >= \epsilon - M \lambda_{ie} is not equivalent to the exact pessimistic IEO loss. For any point whose positive margin is in (0, \epsilon), the constraint with \lambda=0 is infeasible, so the only feasible choice is \lambda=1, which incorrectly treats a provably suboptimal decision as a follower optimum. Because w is continuous and optimized, positive margins can be arbitrarily small, so no a priori choice of \epsilon can separate all of them from zero. Moreover, the text states that M can be set equal to \epsilon or larger; if M=\epsilon, then a point with a negative margin cannot be represented by either \lambda=0 or \lambda=1, making the master problem infeasible for valid lower-level optimal points. The paper itself calls formulation (14) an \epsilon-approximation, but Contribution 1 claims minimization of 'the true pessimistic IEO loss without relying on approximations or surrogate functions.' As stated, the claim is not supported: the method solves an \epsilon-perturbed problem, and the experiments benchmark that perturbed objective. The value of \epsilon used in the experiments is also never reported, so the results are not reproducible in this respect.
[Section 3.2, Lemma 2] Lemma 2 states that Algorithm 1 converges to a pessimistic IEO solution whose gap from the optimal is at most \Delta. The proof shows that if no new subproblem points are added, then LB \geq UB, where LB comes from P^{(k)}_\epsilon. However, because $P^{(k)}_\epsilon$ is an \epsilon-approximation and not a valid lower-bound relaxation of the original problem (as discussed above), LB is not guaranteed to be a valid lower bound on the true pessimistic objective. Consequently, the stopping criterion UB - LB \leq \Delta does not certify \Delta-optimality for the original pessimistic bilevel problem; it certifies only distance to the \epsilon-perturbed master problem. The lemma therefore needs to be restated with explicit dependence on \epsilon, and a correct error bound must account for the misclassification of margins in (0,\epsilon).
[Section 4.3, Tables 2 and 3, and Section 5] The conclusion claims that 'the proposed IEO method outperforms both LR and SPO+ in terms of out-of-sample IEO loss,' but the data in Tables 2 and 3 do not support a consistent outperformance. For example, in Table 2 with n=100, \delta=1, instance 0, IEO has out-of-sample %\bar{\ell}_{IEO}=1.056 while LR achieves 0.954; in the same table, n=100, \delta=7, \delta=1, IEO has 1.960 versus LR's 0.726. The text in Section 4.3 explicitly acknowledges that 'no method consistently outperforms the others.' The Conclusion and Contribution 3 therefore overstate the experimental evidence. The claims should be qualified to specific regimes (e.g., \delta=3 or \delta=5, or after regularization with LHS), or the tables and conclusion should be aligned with the observed results.
[Section 4.4, Figure 2] The n=500 results for the ny=20 instances are excluded because 'these were the cases where IEO successfully improved the warm-start solutions provided to the solver within a time limit of 1800 seconds.' This exclusion removes the cases where the proposed method may not have improved over its warmstart, which are exactly the unfavorable cases for the claim of consistent outperformance. The exclusion should either be reported as a limitation in the main claim, or the n=500 results should be included (even if they show IEO not improving). As presented, the selective exclusion weakens the conclusion that IEO outperforms LR and SPO+ for larger instances.

minor comments (5)

[Abstract and Section 1] The abstract says the method 'solves an \epsilon-approximation' of the pessimistic bilevel problem, while Contribution 1 says the method minimizes 'the true pessimistic IEO loss without relying on approximations.' These statements are inconsistent; even if the \epsilon issue were resolved, the wording should be aligned.
[Section 3.4.1] The bounds fmin and fmax in the linearization (16) are never specified or discussed in the experiments. Their choice can affect the validity of the linearization, and the paper should report how they are set and whether they are data-dependent.
[Section 3.4.4] The symbol \gamma is used both for the lasso regularization coefficient (Section 4.3, set to 0.005) and for the perturbation scalar in (w = w_j + \gamma\epsilon\epsilon\epsilon). This overloading is confusing; different notation should be used for the two parameters.
[Sections 3.4.2 and 3.4.3] The algorithm parameters ninit, nrep, and nEP are introduced but no values are reported in the computational experiments, except indirectly. Without these values, the experiments are not fully reproducible.
[Section 4.2, Table 1] In Table 1, the 'gap' columns report solver gaps for the branch-and-cut and CCG methods. For Instance 1 with n=500, the branch-and-cut gap is 0.347, which is quite large; the text should be careful when claiming that the branch-and-cut 'solves the problem to optimality' without noting that this only occurs for Instance 10.

Circularity Check

0 steps flagged · score 1.0 of 10

No circularity: the IEO predictor is fit by minimizing a stated loss and tested on independent samples; the epsilon-approximation is a correctness caveat, not a circular reduction.

full rationale

The paper's derivation chain is self-contained and does not reduce to its inputs. The predictor f_w is fit by minimizing the normalized pessimistic IEO loss (7)/(8) over training data, and out-of-sample performance is measured with the same normalized loss on an independent test set; this is the standard decision-focused objective, not a fitted parameter renamed as a prediction. The key reformulation (13)-(14) is an explicit epsilon-approximation of a valid relaxation borrowed from external work [25], and the paper itself states in Section 3.2 that 'formulation (14) is an epsilon-approximation of a valid relaxation of (10), which is, at the same time, a valid relaxation of the original problem (8).' Thus the claimed exactness in Contribution 1 ('minimizing the true pessimistic IEO loss without relying on approximations') is overstated relative to the abstract's epsilon-approximation statement, and the choice of epsilon in constraint (14c) is an unresolved correctness parameter; however, these are accuracy/consistency issues, not circularity. The only self-citation ([4], Pagnoncelli et al.) appears in a list of portfolio-optimization examples and is not load-bearing for any derivation. No fitted constant is reused as a prediction, no uniqueness theorem from the authors is invoked, and no known result is renamed. The computational benchmarks are external (0-1 knapsack instances from [15]) and compare against LR and SPO+, so the empirical claims are independent of the method's own assumptions.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the finite enumeration of the 0-1 feasible set, on the tightness of Zeng's relaxation, and on the ability of a fixed epsilon to represent the strict follower optimality disjunction. None of these are established with full formal proof in this paper. There are no invented entities.

free parameters (5)

epsilon approximation tolerance in (14c) = not specified
Controls strictness of the follower optimality condition. No rule is given for choosing it. An overly large epsilon can include points whose true cost margin is smaller than epsilon, changing the pessimistic objective.
nEP maximum points per sample = not specified
Limits the number of lambda variables in branch-and-cut. Correctness requires e(i) < nEP at termination, but the values used in experiments are not reported.
fmin and fmax bounds for linearization = not specified
The linearization (16) requires finite bounds on the predicted cost components. No values are given for the experiments.
lasso regularization coefficient gamma = 0.005
Used for IEO in Section 4.3 Table 3. This hyperparameter affects the fitted predictor and the out-of-sample results.
warmstart points ninit and perturbations nrep = not specified
Warmstart and cut generation settings influence how many points are added and can affect both runtime and solution quality.

assumptions (6)

domain assumption The feasible set Z of the 0-1 knapsack DOP is finite and can be enumerated for the tested instances.
The relaxation (11) and branch-and-cut algorithm rely on F(Z), the full enumeration of feasible points. Enumeration is only practical for small instances.
domain assumption The relaxation (10) from Zeng [25] is valid and tight for the pessimistic bilevel problem.
Section 3.1 states the tightness argument. The algorithm inherits this result without an independent formal proof in this paper.
standard math For any selected z_i_bar, the set of follower optimal solutions is characterized by fw(xi)^T(z - z_i_bar) <= 0.
This inequality defines the relaxed follower set in (10d) and is used to build the master problem.
ad hoc to paper A fixed epsilon can replace the strict inequality fw(xi)^T(ze - z_i_bar) > 0 in the disjunction (13).
Constraint (14c) imposes >= epsilon for lambda=0. No guarantee is given that epsilon is smaller than all relevant nonzero margins, so the master problem may include or exclude follower optima incorrectly.
domain assumption The synthetic data generator from [15] is representative of contextual optimization settings.
Out-of-sample conclusions are based only on this generator and on 0-1 knapsack instances.
domain assumption Linear predictors fw(x) = Wx are sufficient to capture the relationship between features and costs.
All experiments use linear predictors. Misspecification is only varied through the exponent delta in the generator.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Pessimistic bilevel optimization approach for decision-focused learning." pith.science (2026). https://pith.science/paper/JTIHMTXB

@misc{pith2026250116826,
  author       = {Pith},
  title        = {Pith review of: Pessimistic bilevel optimization approach for decision-focused learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JTIHMTXB}},
  note         = {Machine review of arXiv:2501.16826}
}

abstract

The recent interest in contextual optimization problems, where randomness is associated with side information, has led to two primary strategies for formulation and solution. The first, estimate-then-optimize, separates the estimation of the problem's parameters from the optimization process. The second, decision-focused optimization, integrates the optimization problem's structure directly into the prediction procedure. In this work, we propose a pessimistic bilevel approach for solving general decision-focused formulations of combinatorial optimization problems. Our method solves an $\varepsilon$-approximation of the pessimistic bilevel problem using a specialized cut generation algorithm. We benchmark its performance on the 0-1 knapsack problem against estimate-then-optimize and decision-focused methods, including the popular SPO+ approach. Computational experiments highlight the proposed method's advantages, particularly in reducing out-of-sample regret.

Figures

Figures reproduced from arXiv: 2501.16826 by the authors.

**Figure 1.** Out–of–sample results, ny = 10, ntest = 1000. formance. For δ = 3, as with the case of ny = 10, SPO+ shows the worst performance, while LR and IEO achieve comparable average ¯ℓIEO loss values. Finally, for δ = 5, IEO outperforms both LR and SPO+, with SPO+ showing the poorest performance. It is worth noting that, for n = 400, similar results were observed due to IEO’s difficulty in improving the warmstart solutions … view at source ↗

**Figure 2.** Out–of–sample results, ny = 20, ntest = 1000. function value), enabling the computation of estimators with lower in-sample ¯ℓIEO values within the same time limit. Furthermore, numerical experiments on the 0–1 knapsack problem demonstrate that the proposed IEO method outperforms both LR and SPO+ in terms of out-of-sample IEO loss. Additionally, IEO exhibits robustness against model misspecification, unlike LR and … view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

29 extracted references · 25 canonical work pages

[1]

End-to-end learning of user equilibrium with implicit neural networks,

Z. Liu, Y. Yin, F. Bai, and D. K. Grimm, “End-to-end learning of user equilibrium with implicit neural networks,”Transportation Research Part C: Emerging Technologies, 23 vol. 150, p. 104085, 2023

work page 2023
[2]

Optimizing Inventory Routing: A Decision-Focused Learning Approach using Neural Networks

M. S. Islam and A. T. Wasi, “Optimizing inventory routing: A decision-focused learning approach using neural networks,” arXiv preprint arXiv:2311.00983 , 2023

work page Pith review arXiv 2023
[3]

Stock movement prediction from tweets and historical prices,

Y. Xu and S. B. Cohen, “Stock movement prediction from tweets and historical prices,” in Proceedings of the 56th Annual Meeting of the Association for Computational Linguis- tics (Volume 1: Long Papers) (I. Gurevych and Y. Miyao, eds.), (Melbourne, Australia), pp. 1970–1979, Association for Computational Linguistics, 2018

work page 1970
[4]

A synthetic data-plus- features driven approach for portfolio optimization,

B. K. Pagnoncelli, D. Ram ´ ırez, H. Rahimian, and A. Cifuentes, “A synthetic data-plus- features driven approach for portfolio optimization,” Computational Economics, vol. 62, no. 1, pp. 187–204, 2023

work page 2023
[5]

Stock movement and volatility prediction from tweets, macroeconomic factors and historical prices,

S. Wang, Y. Bai, T. Ji, K. Fu, L. Wang, and C.-T. Lu, “Stock movement and volatility prediction from tweets, macroeconomic factors and historical prices,” arXiv preprint arXiv:2312.03758, 2023

arXiv 2023
[6]

A modified ctgan- plus-features-based method for optimal asset allocation,

J.-M. Pe˜ na, F. Su´ arez, O. Larr´ e, D. Ram ´ ırez, and A. Cifuentes, “A modified ctgan- plus-features-based method for optimal asset allocation,” Quantitative Finance, vol. 24, no. 3-4, pp. 465–479, 2024

work page 2024
[7]

A survey of contextual optimization methods for decision making under uncertainty,

U. Sadana, A. Chenreddy, E. Delage, A. Forel, E. Frejinger, and T. Vidal, “A survey of contextual optimization methods for decision making under uncertainty,”arXiv preprint arXiv:2306.10374, 2023

arXiv 2023
[8]

From predictive to prescriptive analytics,

D. Bertsimas and N. Kallus, “From predictive to prescriptive analytics,” Management Science, vol. 66, no. 3, pp. 1025–1044, 2020

work page 2020

Show all 29 references

[9]

Estimate-then-optimize versus integrated-estimation-optimization versus sample average approximation: A stochastic dominance perspective,

A. N. Elmachtoub, H. Lam, H. Zhang, and Y. Zhao, “Estimate-then-optimize versus integrated-estimation-optimization versus sample average approximation: A stochastic dominance perspective,” arXiv preprint arXiv:2304.06833 , 2023

2023 arXiv
[10]

Decision-focused learning: Foundations, state of the art, benchmark and future oppor- tunities,

J. Mandi, J. Kotary, S. Berden, M. Mulamba, V. Bucarey, T. Guns, and F. Fioretto, “Decision-focused learning: Foundations, state of the art, benchmark and future oppor- tunities,” 2024

2024
[11]

A bilevel framework for decision-making under uncertainty with contextual information,

M. Mu˜ noz, S. Pineda, and J. Morales, “A bilevel framework for decision-making under uncertainty with contextual information,” Omega, vol. 108, p. 102575, 2022

2022
[12]

The big data newsvendor: Practical insights from machine learning,

G.-Y. Ban and C. Rudin, “The big data newsvendor: Practical insights from machine learning,” Operations Research, vol. 67, no. 1, pp. 90–108, 2019. 24

2019
[13]

Smart “predict, then optimize

A. N. Elmachtoub and P. Grigas, “Smart “predict, then optimize”,” Management Sci- ence, vol. 68, no. 1, pp. 9–26, 2022

2022
[14]

Decision-focused predictions via pessimistic bilevel optimization: A computational study,

V. Bucarey, S. Calder´ on, G. Mu˜ noz, and F. Semet, “Decision-focused predictions via pessimistic bilevel optimization: A computational study,” in Integration of Con- straint Programming, Artificial Intelligence, and Operations Research (B. Dilkina, ed.), (Cham), pp. 127–135,...

2024
[15]

Risk guarantees for end-to-end prediction and optimization processes,

N. Ho-Nguyen and F. Kılın¸ c-Karzan, “Risk guarantees for end-to-end prediction and optimization processes,” Management Science, vol. 68, no. 12, pp. 8680–8698, 2022

2022
[16]

Smart predict-then-optimize for two-stage linear programs with side information,

A. S. Estes and J.-P. P. Richard, “Smart predict-then-optimize for two-stage linear programs with side information,” INFORMS Journal on Optimization , 2023

2023
[17]

Smart predict-and-optimize for hard combinatorial optimization problems,

J. Mandi, E. Demirovi´ c, P. J. Stuckey, and T. Guns, “Smart predict-and-optimize for hard combinatorial optimization problems,” arXiv preprint arXiv:1911.10092 , 2019

1911 arXiv
[18]

Pessimistic bilevel op- timization,

W. Wiesemann, A. Tsoukalas, P.-M. Kleniati, and B. Rustem, “Pessimistic bilevel op- timization,” SIAM Journal on Optimization , vol. 23, no. 1, pp. 353–380, 2013

2013
[19]

Connections and reformulations between robust and bilevel optimization,

M. Goerigk, J. Kurtz, M. Schmidt, and J. Th¨ urauf, “Connections and reformulations between robust and bilevel optimization,” Optmization online , 2024

2024
[20]

Pessimistic bilevel linear optimization,

S. Dempe, G. Luo, and S. Franke, “Pessimistic bilevel linear optimization,” Journal of Nepal Mathematical Society, vol. 1, p. 1–10, Feb. 2018

2018
[21]

A survey on mixed-integer program- ming techniques in bilevel optimization,

T. Kleinert, M. Labb´ e, I. Ljubi´ c, and M. Schmidt, “A survey on mixed-integer program- ming techniques in bilevel optimization,” EURO Journal on Computational Optimiza- tion, vol. 9, p. 100007, 2021

2021
[22]

Parametric integer programming algorithm for bilevel mixed integer programs,

M. K¨ oppe, M. Queyranne, and C. T. Ryan, “Parametric integer programming algorithm for bilevel mixed integer programs,” Journal of Optimization Theory and Applications , vol. 146, 2010

2010
[23]

A new general-purpose algorithm for mixed-integer bilevel linear programs,

M. Fischetti, I. Ljubi´ c, M. Monaci, and M. Sinnl, “A new general-purpose algorithm for mixed-integer bilevel linear programs,” Operations Research, vol. 65, no. 6, pp. 1615– 1637, 2017

2017
[24]

A branch-and-cut algorithm for mixed integer bilevel linear optimization problems and its implementation,

S. Tahernejad, T. K. Ralphs, and S. T. DeNegre, “A branch-and-cut algorithm for mixed integer bilevel linear optimization problems and its implementation,” Mathemat- ical Programming Computation, vol. 12, 2020. 25

2020
[25]

A practical scheme to compute the pessimistic bilevel optimization problem,

B. Zeng, “A practical scheme to compute the pessimistic bilevel optimization problem,” INFORMS Journal on Computing , vol. 32, no. 4, pp. 1128–1142, 2020

2020
[26]

Polyhedron representation transformation algorithm,

T. Christof and A. L¨ obel, “Polyhedron representation transformation algorithm,” 2015. Software available from https://porta.zib.de/

2015
[27]

A systematic review on overfitting control in shallow and deep neural networks,

M. M. Bejani and M. Ghatee, “A systematic review on overfitting control in shallow and deep neural networks,” Artificial Intelligence Review, vol. 54, no. 8, pp. 6391–6438, 2021

2021
[28]

Overfitting, model tuning, and evaluation of prediction performance,

O. A. Montesinos L´ opez, A. Montesinos L´ opez, and J. Crossa, “Overfitting, model tuning, and evaluation of prediction performance,” in Multivariate statistical machine learning methods for genomic prediction , pp. 109–139, Springer, 2022

2022
[29]

Holistic robust data-driven decisions,

A. Bennouna and B. V. Parys, “Holistic robust data-driven decisions,” arXiv preprint arXiv:2207.09560, 2023. 26

2023 arXiv

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [1]

End-to-end learning of user equilibrium with implicit neural networks,

Z. Liu, Y. Yin, F. Bai, and D. K. Grimm, “End-to-end learning of user equilibrium with implicit neural networks,”Transportation Research Part C: Emerging Technologies, 23 vol. 150, p. 104085, 2023

work page 2023

[2] [2]

Optimizing Inventory Routing: A Decision-Focused Learning Approach using Neural Networks

M. S. Islam and A. T. Wasi, “Optimizing inventory routing: A decision-focused learning approach using neural networks,” arXiv preprint arXiv:2311.00983 , 2023

work page Pith review arXiv 2023

[3] [3]

Stock movement prediction from tweets and historical prices,

Y. Xu and S. B. Cohen, “Stock movement prediction from tweets and historical prices,” in Proceedings of the 56th Annual Meeting of the Association for Computational Linguis- tics (Volume 1: Long Papers) (I. Gurevych and Y. Miyao, eds.), (Melbourne, Australia), pp. 1970–1979, Association for Computational Linguistics, 2018

work page 1970

[4] [4]

A synthetic data-plus- features driven approach for portfolio optimization,

B. K. Pagnoncelli, D. Ram ´ ırez, H. Rahimian, and A. Cifuentes, “A synthetic data-plus- features driven approach for portfolio optimization,” Computational Economics, vol. 62, no. 1, pp. 187–204, 2023

work page 2023

[5] [5]

Stock movement and volatility prediction from tweets, macroeconomic factors and historical prices,

S. Wang, Y. Bai, T. Ji, K. Fu, L. Wang, and C.-T. Lu, “Stock movement and volatility prediction from tweets, macroeconomic factors and historical prices,” arXiv preprint arXiv:2312.03758, 2023

arXiv 2023

[6] [6]

A modified ctgan- plus-features-based method for optimal asset allocation,

J.-M. Pe˜ na, F. Su´ arez, O. Larr´ e, D. Ram ´ ırez, and A. Cifuentes, “A modified ctgan- plus-features-based method for optimal asset allocation,” Quantitative Finance, vol. 24, no. 3-4, pp. 465–479, 2024

work page 2024

[7] [7]

A survey of contextual optimization methods for decision making under uncertainty,

U. Sadana, A. Chenreddy, E. Delage, A. Forel, E. Frejinger, and T. Vidal, “A survey of contextual optimization methods for decision making under uncertainty,”arXiv preprint arXiv:2306.10374, 2023

arXiv 2023

[8] [8]

From predictive to prescriptive analytics,

D. Bertsimas and N. Kallus, “From predictive to prescriptive analytics,” Management Science, vol. 66, no. 3, pp. 1025–1044, 2020

work page 2020