Structured Differentiable Optimization for Efficient Decision-focused Learning in Power Systems

Fei Teng; Wangkun Xu

REVIEW 2 major objections 5 minor 41 references

Structured Differentiable Optimization for Efficient Decision-focused Learning in Power Systems

T0 review · 2 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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

Pith's one-line read DiffAPQP shows that structuring the optimization layer as an affine-parametric QP with cached forward solves and a reduced-KKT backward pass makes decision-focused power-system training several times faster at nearly unchanged operating…

desk verdict Solid, well-engineered differentiable QP layer for DfL with honest benchmarking; the degeneracy at zero renewable forecasts is openly disclosed but under-quantified. read the letter →

arxiv 2608.04189 v1 pith:FSR6DVCS submitted 2026-08-04 eess.SY cs.SY

Wangkun Xu , Fei Teng This is my paper · ORCID

classification eess.SYcs.SY MSC 90C2090C31

keywords decision-focusedlearningdifferentiableoptimizationaffine-parametricquadraticprogrameconomicdispatchredispatchimplicitdifferentiationKKTreductionwarmstarting

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

Decision-focused learning trains a forecaster against the cost of the operational decisions it feeds, but it is usually too slow for realistic networks because every training step must solve and differentiate a large optimization problem. This paper claims that the cost can be reclaimed by keeping the optimization layer in the form of an affine-parametric quadratic program, where forecasts enter through fixed affine maps, and by exploiting the fact that training repeatedly solves the same template: solver factorizations and warm-start iterates are reused across samples and epochs. For the backward pass, the paper proves that differentiating the full KKT system is equivalent to differentiating a smaller reduced system built only from the active inequality constraints, and that for losses depending only on the optimal value an envelope-theorem formula supplies the gradient without any adjoint solve. On the IEEE 118-bus system with a 24-hour economic-dispatch and redispatch horizon, this combination trims the fastest measured epoch times by factors of about 3.9 (closed loop) and 6.4 (counterfactual) while roughly halving peak memory and keeping operating costs within about 0.2% of the reference. If the claims hold, decision-focused learning moves from small test systems toward operational-scale power-system training.

What carries the argument

The central object is the affine-parametric quadratic program (APQP), a QP whose linear objective coefficient $q(\hat{y})$ and constraint right-hand sides $b(\hat{y}), h(\hat{y})$ are affine in the forecast parameters, so that all gradients with respect to the forecasts are analytic. The load-bearing mechanism is the reduced KKT system $K_s$ built from $P$, $A$, and the active rows $G_{\mathcal{A}}$ after eliminating inactive inequalities; the paper proves its solution equals the full system's derivative. For value-function losses, the envelope theorem gives $D_{\hat{y}_i} \alpha = z^\top Q_i + d_i - \nu^\top B_i - \lambda^\top H_i$ directly from the stored primal-dual solution. Because the KKT matrix is constant across training solves, factorization caching and warm-starting accelerate the forward pass.

What would settle it

Run the same 118-bus batch through full-KKT and reduced-KKT adjoints while sweeping the active-set tolerance from $10^{-7}$ to $10^{-2}$ and record gradient cosine similarity; a sharp drop below 0.99, or a divergence in training cost, would show where the reduction misclassifies constraints. Separately, count the fraction of training samples with zero renewable forecasts at which both curtailment bounds bind; if that fraction is nontrivial, the non-unique gradients at those points are a measurable part of the training signal and the speedup claims should be reported conditional on those samples.

Watch

Extended reading notes

Core claim

DiffAPQP's central claim is that the derivative of a QP solution map can be obtained from a reduced equality-constrained KKT system built from the active inequalities, and that this reduced derivative is exactly the full-KKT derivative provided strict complementarity and LICQ hold; the same holds for LPs at a non-degenerate vertex. This replaces an asymmetric adjoint system of dimension $n_d+n_{\mathrm{eq}}+n_{\mathrm{in}}$ with a symmetric system of dimension $n_d+n_{\mathrm{eq}}+|\mathcal{A}|$, solvable by MINRES, and it removes the inactive complementarity rows that make the full system ill-conditioned. When the training loss depends only on the optimal value, the paper further proves an envelope-theorem identity $D_{y_i} \alpha = z^\top Q_i + d_i - \nu^\top B_i - \lambda^\top H_i$, so the backward pass needs no adjoint linear solve at all. On the IEEE 118-bus system with a 24-hour economic-dispatch and redispatch horizon, the fastest configurations take closed-loop epochs from 38.65 to 9.55 minutes and counterfactual epochs from 10.73 to 1.68 minutes, roughly halve peak memory, and keep operating costs within about 0.2% of the baseline. To the authors' knowledge this is the first solver-based end-to-end decision-focused learning demonstration at that scale.

Load-bearing premise

The reduced-KKT backward pass is only as correct as the numerically identified active set, and it assumes strict complementarity and LICQ at the optimum; at degenerate points such as zero renewable forecasts where both curtailment bounds are active, the gradient is not unique, and the paper reports its main speedups without quantifying how often such degeneracies occur in the 118-bus data.

Editorial extensions

If this is right

End-to-end decision-focused learning becomes practical at operational scale: the 118-bus, 24-hour dispatch-redispatch case trains in minutes per epoch instead of tens of minutes.
Because the optimization layer dominates epoch time, the speedups benefit any training loop that repeatedly solves the same convex program, not just power-system economic dispatch and redispatch.
Value-function training losses can be differentiated almost for free, so counterfactual learning is no longer bottlenecked by the backward pass.
Reduced-KKT gradients match the full-KKT gradients closely (mean cosine similarity above 0.997 in controlled first-batch comparisons), indicating the learning signal is preserved.
Peak memory savings of roughly 50%, with even larger savings in counterfactual runs, allow larger models or batches on the same hardware.

Reading between the lines

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

Going beyond the paper's testbed, the same affine-parametric structure appears in model predictive control, portfolio optimization, and market bidding, so the repeated-solve caching and reduced-KKT backward pass should transfer to any fixed-template differentiable optimization loop; a direct test would be to benchmark those tasks with the same layer.
The envelope-theorem gradient suggests a general design pattern: whenever a training loss is a function of the optimal value rather than the optimal decision, backward differentiation can be made nearly free, which invites custom cost-aware losses whose gradients can be validated by finite differences.
The active-set tolerance is effectively a hyperparameter of the reduced-KKT method; an adaptive tolerance schedule could reduce the impact of degenerate points such as zero renewable forecasts, where both curtailment bounds bind and the gradient is non-unique.
The reported speedups are measured on CPU under a fixed core cap; on accelerator hardware or with unrolled solver differentiation the trade-offs between forward reuse and backward structure may shift, so the practical advantage on GPUs remains an open question.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

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

Xu and Teng have built a genuine workhorse: a differentiable affine-parametric QP layer that parses CVXPY models, caches solver factorizations, warm-starts across epochs, and gives both a reduced-KKT adjoint and an envelope-theorem value gradient. The engineering is thorough, the open-source release is real, and the benchmarking against CvxpyLayers is honestly matched (same solvers, same tolerances, cores capped). The speedups—2–4x closed-loop, faster counterfactual—are credible. The proof that full and reduced KKT differentiation coincide under strict complementarity and LICQ is standard but cleanly executed, and Proposition 3 correctly identifies the value-gradient as a subgradient at non-differentiable points rather than overclaiming.

The main soft spot is exactly the one the stress-test note lands on: the degeneracy at zero renewable forecasts. When b_solar = 0, both curtailment bounds are active, LICQ fails, K_s is singular, and the gradient is non-unique. Appendix E openly says this and then reports gradient fidelity only over positive forecasts. That is honest, but it leaves the central training-signal claim unquantified: we don't know how often these degenerate points occur in the 255 training samples, nor whether the arbitrary dual selection systematically biases the DfL update. Nighttime solar is pervasive, so this is not a corner case. The speedup numbers and the 0.2% cost-parity claim are empirical and likely robust, but the paper should report the frequency of singular K_s and show that excluding those points does not change the cost comparison.

The LP discussion in the appendix is a second, milder soft spot: q-gradients depend on which optimal primal the solver returns. The authors note this honestly and show regularization helps, but the main text's claim of similar operating costs is only tested on the QP cases; the LP behavior is left for the appendix. Minor.

The citation pattern looks fine; connecting to the DfL power-systems literature and dQP/BPQP is accurate. There are a few self-citations, but they are to the authors' own GridForge and E2E-AT framework, which are legitimately the tools used.

Verdict: this deserves referee time. It is a useful piece of infrastructure with an honest, well-executed evaluation. I would send it to review with a request to quantify the degeneracy frequency and its effect on the reported gradients and costs. The claims as stated are probably right, but they are not yet fully pinned down.

Referee Report

2 major / 5 minor

Summary. The paper presents DiffAPQP, an open-source framework for differentiable affine-parametric quadratic programs (APQPs) aimed at decision-focused learning (DfL) in power systems. The forward pass automatically canonicalizes CVXPY models into APQP form and accelerates repeated solves through solver warm-start and solver-data update. The backward pass offers full-KKT and reduced-KKT implicit differentiation, with a proof that eliminating inactive inequalities from the adjoint system is equivalent to the full system under LICQ, strict complementarity, and second-order sufficient conditions; for value-function losses, an envelope-theorem gradient avoids the adjoint solve altogether. Experiments on the IEEE 118-bus system with a 24-hour coupled economic-dispatch and redispatch horizon report 2.27x--3.58x closed-loop and 3.62x--4.38x counterfactual training speedups over CvxpyLayers under matched SCS and Clarabel backends, roughly 50% peak-memory reduction, and test operating costs within 0.2% of CvxpyLayers.

Significance. If the open issues are resolved, this is a valuable contribution with a sound theoretical core and unusually careful empirical methodology. The APQP canonicalization removes a real usability bottleneck; the reduced-KKT equivalence is standard perturbation analysis but is proved cleanly; the value-function gradient is a correct application of the envelope theorem rather than circular reuse of the forward solve. The evaluation is exemplary in matching solver backends, capping CPU cores, reporting decomposed timings, and measuring gradient fidelity, with open-source code. The main risk is that the gradient-fidelity analysis explicitly excludes degenerate zero-renewable forecasts, which are likely systematic in a 24-hour solar-wind horizon, leaving the exactness of the training signal at those points unquantified.

major comments (2)

[Appendix E, Tables VI-VII] Appendix E explicitly acknowledges that zero renewable forecasts create simultaneously active curtailment bounds (0 <= p_curtail <= b_solar with b_solar = 0) and that the derivative need not be unique; Tables VI and VII consequently report gradient similarity only for 'Solar>0' and 'Wind>0'. Since the 24-hour ED/RD horizon includes night hours and the forecaster outputs are clamped to nonnegative values before entering the optimization, this degeneracy is plausibly systematic rather than rare in the 255 training samples. The paper does not report the frequency of degenerate samples, the number of singular reduced-KKT systems encountered, or how the solver-selected dual at a degenerate point affects the value-function gradient. Table VII's value-function solar mean cosine of 0.7138 with P05 of 0.0507 is attributed to training-path divergence and mask mismatch, but degeneracy is a competing explanation that is not ruled out. This matters for the claim that DiffAPQP matches CvxpyLayers' training signal within 0.2% cost: at these points the 'free' gradient is a subgradient selected by solver internals. Please quantify the degeneracy frequency and either verify that the clamp blocks backpropagation at all such samples or report gradient fidelity on degenerate samples separately.
[Section IV-B, Eq. (16), Table VI] The reduced-KKT equivalence in Proposition 1 assumes exact active-set identification via strict complementarity and LICQ, but the implementation identifies the active set through numerical tolerances (epsilon_abs, epsilon_rel). A misclassified constraint changes the reduced derivative matrix K_s, and an over-inclusive tolerance can make K_s singular. The controlled single-batch comparison in Table VI is a useful first step, but it covers only 32 samples before any optimizer update and does not report how often active-set misclassification occurs over the full 255-sample training set or across epochs. Given that the power-system model contains exactly binding curtailment, ramping, and line-limit constraints, please report the distribution of |G_j z* - h_j| on the ED/RD training data and the sensitivity of the reduced-KKT gradients to the active-set tolerance, for example a sweep over epsilon_abs in the appendix.

minor comments (5)

[Abstract] The phrase 'resulting in eligible backward time' appears to be a typo for 'negligible backward time'.
[Section III-C2] The text alternates between 'work space' and 'workspace'; please use one term and clarify how the reused KKT factorization is stored across solvers and how its memory footprint is bounded.
[Section V-A vs. Appendix C3] Section V-A states that solar and wind forecasts are 'restricted to positive values' before the optimization layers, while Appendix C3 says they are 'constrained to be nonnegative'; please make the exact clamping operation explicit and consistent.
[Tables VI and VII] The columns 'Solar>0' and 'Wind>0' should be accompanied by the number of samples excluded at each epoch, since the mask reconstructed from the initial AbL forecaster may not match later forecasts, as the text itself acknowledges.
[Fig. 3] The inset panels have very small fonts and no labeled axes; please enlarge them or describe in the caption what quantity is plotted on the y-axis.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: core derivative formulas are standard implicit-differentiation and envelope-theorem results with self-contained proofs, and all speedups are external wall-clock benchmarks.

full rationale

DiffAPQP's derivation chain is self-contained and benchmarked externally. The full-KKT adjoint (11)-(14) is standard implicit differentiation of the KKT conditions, and the reduced system (16)-(18) is proven equivalent to it in Proposition 1 under A1-A4, with a self-contained proof in Appendix A; the LP case (Proposition 2) likewise carries its own proof. The value-function gradient (19) is the textbook envelope/Danskin sensitivity formula, derived in the paper (Proposition 3) and citable to Boyd and Vandenberghe; reusing the forward primal-dual solution for the backward pass is the correct application of the envelope theorem, not a fitted-input-called-prediction step. No parameters are fitted to the claimed speedups or cost comparisons; the 2.27x-3.58x and 3.62x-4.38x results are wall-clock measurements against CvxpyLayers under matched SCS/Clarabel backends and seeds, and memory/cost differences are measured. Self-citations ([3], [4], [12], [13]) provide background, the data-generation package GridForge, and prior DfL settings; none is invoked as the uniqueness or correctness argument for the paper's central claims, so they are not load-bearing. The acknowledged degeneracy at zero renewable forecasts (Appendix E: "At a zero renewable forecast, the lower and upper curtailment bounds are simultaneously active... resulting in a degenerate KKT point") and the corresponding restriction of gradient-fidelity statistics to Solar>0 and Wind>0 are honest limitations about non-unique subgradients, and Proposition 3 explicitly frames the value gradient as a subgradient at such points; this is a correctness/robustness caveat, not a circular reduction. Therefore no circular step is exhibited.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The mathematical derivation is self-contained and uses standard convex-analysis machinery. The main numerical freedom is the active-set tolerance and adjoint solver tolerances, which are experimental hyperparameters rather than fitted physical constants. No new entities are introduced.

free parameters (3)

active_set_tolerance = eps_abs=1e-3, eps_rel=0 in random benchmarks; not specified for the power-system experiments
The reduced-KKT backward pass requires identifying active inequality constraints. The tolerance determines which constraints enter the reduced system, and an overly large tolerance can make the reduced KKT singular.
adjoint solver tolerances = MINRES relative tolerance 1e-9; LSQR abs/rel tolerances 1e-6 with max 5000 iterations
These tolerances affect the numerical fidelity of computed gradients. In Table VI, full-KKT with looser tolerance has lower cosine similarity to CvxpyLayers than reduced-KKT.
LP regularization epsilon = 1e-3 in the appendix LP experiments
Added to LP problems in random benchmarks to ensure solvability and consistent gradients; not used in the main power-system experiments, which are QPs.

assumptions (6)

domain assumption The optimization is an affine-parametric QP: P, A, G are fixed and only q, b, h, c depend affinely on the forecast parameters
The entire DiffAPQP canonicalization and backward-pass acceleration rely on the APQP structure (5). Problems with nonlinear parameter dependence are outside scope.
domain assumption The forward solution satisfies the KKT conditions (A1)
Assumption (A1) is used in Proposition 1 and in the derivation of the full-KKT Jacobian (11). It requires the solver to reach a KKT point.
domain assumption Strict complementarity (A2)
Strict complementarity at the optimum is required for the equivalence of full and reduced KKT in Proposition 1. It can fail at degenerate points such as zero renewable forecasts where both curtailment bounds are active.
domain assumption LICQ at the active constraints (A4)
Linear independence of active constraint gradients is required for non-singularity of the KKT matrices K_a and K_s. Linearly dependent constraints would make the adjoint system singular.
domain assumption Second-order sufficient condition (A3): P is positive definite on the null space of active constraints
This is the standard SOSC for the QP, used to prove non-singularity of the KKT system. For LPs, it is replaced by the non-degenerate vertex assumption (A5).
domain assumption Slater's condition holds for the value-function differentiation (Proposition 3)
Slater's condition is needed to apply Danskin's theorem and guarantee strong duality when deriving the envelope-theorem gradient in equation (19).

how reviews work

0 comments

Cite this review

Pith. "Pith review of Structured Differentiable Optimization for Efficient Decision-focused Learning in Power Systems." pith.science (2026). https://pith.science/paper/FSR6DVCS

@misc{pith2026260804189,
  author       = {Pith},
  title        = {Pith review of: Structured Differentiable Optimization for Efficient Decision-focused Learning in Power Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FSR6DVCS}},
  note         = {Machine review of arXiv:2608.04189}
}

abstract

Decision-focused learning (DfL) trains forecasting models to align downstream decision consequences, such as power-system operating costs. However, its application to realistic power networks is limited by the need to repeatedly solve and differentiate large optimization problems during training. This paper presents DiffAPQP, a solver-flexible framework and open-source Python package for scalable DfL with affine-parametric quadratic programs. To accelerate the forward pass, DiffAPQP automatically canonicalizes quadratic power-system models written in CVXPY into a differentiation-ready representation and takes advantage of the repetitive solving structure through solver warm-start and solver-data update during training. For the backward pass acceleration, we establish the equivalence between differentiation through the full KKT system and a reduced system obtained by eliminating inactive inequality constraints. For training losses depending solely on the optimal value, we further derive an envelope-theorem-based gradient that avoids solving an adjoint KKT system, resulting in eligible backward time. To our knowledge, this work presents the first solver-based end-to-end DfL demonstration on the IEEE 118-bus system with a 24-hour coupled economic-dispatch and redispatch horizon. Under matched SCS and Clarabel backends on a Linux machine, DiffAPQP achieves $2.27\times$--$3.58\times$ closed-loop and $3.62\times$--$4.38\times$ counterfactual end-to-end DfL training speedups over CvxpyLayers. The best solver configurations increase these speedups to $3.91\times$ (from 38.65 to 9.55 min/epoch) and $6.39\times$ (from 10.73 to 1.68 min/epoch), respectively. Additionally, DiffAPQP reduces peak memory usage by approximately $50\%$, while keeping similar operating costs as CvxpyLayers.

Figures

Figures reproduced from arXiv: 2608.04189 by the authors.

**Figure 2.** DiffOpt as part of NN. The forward and backward passes are [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** End-to-end DfL training performances of DiffAPQP compared with CvxpyLayers using SCS and Clarabel solver backends. [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

Figures from the paper (7 more)

**Figure 4.** Figure 4: Brief relationships among the compilers considered in the [PITH_FULL_IMAGE:figures/full_fig_p017_4.png]

**Figure 5.** Figure 5: DiffAPQP forward-pass solution time under cold start (CS), warm start only (WS), update only (UP), and combined warm start and [PITH_FULL_IMAGE:figures/full_fig_p022_5.png]

**Figure 6.** Figure 6: End-to-end runtime of the DiffAPQP solution-map and value-function layers and CvxpyLayers, with stacked bars separating forward [PITH_FULL_IMAGE:figures/full_fig_p023_6.png]

**Figure 7.** Figure 7: Mean sample-wise cosine similarity between DiffAPQP gradients and CvxpyLayers references. For each gradient component [PITH_FULL_IMAGE:figures/full_fig_p024_7.png]

**Figure 8.** Figure 8: Mean effective CPU-core utilization, aggregated over the parent and worker processes during end-to-end forward and backward [PITH_FULL_IMAGE:figures/full_fig_p025_8.png]

**Figure 9.** Figure 9: Estimated end-to-end CPU work in core-seconds, computed as the mean effective cores multiplied by the combined forward [PITH_FULL_IMAGE:figures/full_fig_p026_9.png]

**Figure 10.** Figure 10: Peak increase in system-used memory relative to the pre-construction benchmark baseline, measured during layer initialization [PITH_FULL_IMAGE:figures/full_fig_p027_10.png]

Review history (2 revisions) →

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

41 extracted references · 23 canonical work pages

[1]

Cost-oriented load forecasting,

J. Zhang, Y . Wang, and G. Hug, “Cost-oriented load forecasting,” Electric Power Systems Research, vol. 205, p. 107723, 2022

work page 2022
[2]

Prescribing net demand for two-stage electricity generation scheduling,

J. M. Morales, M. Munoz, and S. Pineda, “Prescribing net demand for two-stage electricity generation scheduling,”Operations Research Perspectives, vol. 10, p. 100268, 2023

work page 2023
[3]

Decision-focused learning for power system decision-making under uncertainty,

H. Zhang, R. Li, Q. Du, J. Tao, S. Pineda, G. Kariniotakis, S. Camal, C. B. Monroc, M. Sun, C. Wan, W. Xu, and F. Teng, “Decision-focused learning for power system decision-making under uncertainty,”IEEE Transactions on Power Systems, vol. 41, no. 1, pp. 307–323, 2026

2026
[4]

Learning-augmented power system operations: A unified optimization view,

W. Xu, Z. Chu, and F. Teng, “Learning-augmented power system operations: A unified optimization view,” 2026. [Online]. Available: https://arxiv.org/abs/2505.05203

arXiv 2026
[5]

Feature-driven economic improvement for network-constrained unit commitment: A closed-loop predict-and-optimize framework,

X. Chen, Y . Yang, Y . Liu, and L. Wu, “Feature-driven economic improvement for network-constrained unit commitment: A closed-loop predict-and-optimize framework,”IEEE Transactions on Power Systems, vol. 37, no. 4, pp. 3104–3118, 2022

2022
[6]

Towards improving unit commitment economics: An add-on tailor for renewable energy and reserve predic- tions,

X. Chen, Y . Liu, and L. Wu, “Towards improving unit commitment economics: An add-on tailor for renewable energy and reserve predic- tions,”IEEE Transactions on Sustainable Energy, vol. 15, no. 4, pp. 2547–2566, 2024

work page 2024
[7]

Task-based end-to-end model learning in stochastic optimization,

P. Donti, B. Amos, and J. Z. Kolter, “Task-based end-to-end model learning in stochastic optimization,”Advances in neural information processing systems, vol. 30, 2017

2017
[8]

A task-based day-ahead load forecasting model for stochastic economic dispatch,

J. Han, L. Yan, and Z. Li, “A task-based day-ahead load forecasting model for stochastic economic dispatch,”IEEE Transactions on Power Systems, vol. 36, no. 6, pp. 5294–5304, 2021

work page 2021

Show all 41 references

[9]

End-to-end learning with multiple modalities for system-optimised renewables nowcasting,

R. V ohra, A. Rajaei, and J. L. Cremer, “End-to-end learning with multiple modalities for system-optimised renewables nowcasting,” in 2023 IEEE Belgrade PowerTech, 2023, pp. 1–8

2023
[10]

Toward value-oriented renewable energy forecasting: An iterative learning approach,

Y . Zhang, M. Jia, H. Wen, Y . Bian, and Y . Shi, “Toward value-oriented renewable energy forecasting: An iterative learning approach,”IEEE Transactions on Smart Grid, 2024

2024
[11]

More than accuracy: end-to- end wind power forecasting that optimises the energy system,

D. Wahdany, C. Schmitt, and J. L. Cremer, “More than accuracy: end-to- end wind power forecasting that optimises the energy system,”Electric Power Systems Research, vol. 221, p. 109384, 2023

2023
[12]

E2e-at: A unified framework for tackling uncertainty in task-aware end-to-end learning,

W. Xu, J. Wang, and F. Teng, “E2e-at: A unified framework for tackling uncertainty in task-aware end-to-end learning,” inProceedings of the AAAI Conference on Artificial Intelligence, vol. 38, no. 14, 2024, pp. 16 220–16 227

2024
[13]

Task-aware machine unlearning and its application in load forecasting,

W. Xu and F. Teng, “Task-aware machine unlearning and its application in load forecasting,”IEEE Transactions on Power Systems, 2024

2024
[14]

Decision-focused linear pooling for probabilistic forecast combination,

A. Stratigakos, S. Pineda, and J. M. Morales, “Decision-focused linear pooling for probabilistic forecast combination,”International Journal of Forecasting, vol. 41, no. 3, pp. 1112–1125, 2025

2025
[15]

On the participation of energy storage systems in reserve markets using decision focused learning,

Á. Paredes, J.-F. Toubeau, J. A. Aguado, and F. Vallée, “On the participation of energy storage systems in reserve markets using decision focused learning,”Sustainable Energy, Grids and Networks, vol. 42, p. 101677, 2025

2025
[16]

Backpropagation of unrolled solvers with folded optimization,

J. Kotary, M. H. Dinh, and F. Fioretto, “Backpropagation of unrolled solvers with folded optimization,”arXiv preprint arXiv:2301.12047, 2023

2023 arXiv
[17]

The elements of differentiable program- ming,

M. Blondel and V . Roulet, “The elements of differentiable program- ming,”arXiv preprint arXiv:2403.14606, 2024

2024 arXiv
[18]

Dif- ferentiating through a cone program,

A. Agrawal, S. Barratt, S. Boyd, E. Busseti, and W. M. Moursi, “Dif- ferentiating through a cone program,”arXiv preprint arXiv:1904.09043, 2019

1904 arXiv
[19]

CVXPY: A Python-embedded modeling lan- guage for convex optimization,

S. Diamond and S. Boyd, “CVXPY: A Python-embedded modeling lan- guage for convex optimization,”Journal of Machine Learning Research, vol. 17, no. 83, pp. 1–5, 2016

2016
[20]

Operator splitting for a homogeneous embedding of the linear complementarity problem,

B. O’Donoghue, “Operator splitting for a homogeneous embedding of the linear complementarity problem,”SIAM Journal on Optimization, vol. 31, no. 3, pp. 1999–2023, 2021

1999
[21]

Clarabel: An interior-point solver for conic programs with quadratic objectives,

P. J. Goulart and Y . Chen, “Clarabel: An interior-point solver for conic programs with quadratic objectives,” 2024

2024
[22]

Differentiable Optimization-Based Modeling for Machine Learning,

B. Amos, “Differentiable Optimization-Based Modeling for Machine Learning,” Ph.D. dissertation, Carnegie Mellon University, May 2019

2019
[23]

Melding the data-decisions pipeline: Decision-focused learning for combinatorial optimization,

B. Wilder, B. Dilkina, and M. Tambe, “Melding the data-decisions pipeline: Decision-focused learning for combinatorial optimization,” in Proceedings of the AAAI conference on artificial intelligence, vol. 33, no. 01, 2019, pp. 1658–1665

2019
[24]

Toward cost-oriented forecasting of wind power generation,

G. Li and H.-D. Chiang, “Toward cost-oriented forecasting of wind power generation,”IEEE Transactions on Smart Grid, vol. 9, no. 4, pp. 2508–2517, 2018

2018
[25]

Learning joint models of prediction and optimization,

J. Kotary, V . Di Vito, J. Christopher, P. Van Hentenryck, and F. Fioretto, “Learning joint models of prediction and optimization,” inECAI 2024. IOS Press, 2024, pp. 2476–2483

2024
[26]

Bpqp: A differentiable convex optimization framework for efficient end-to-end learning,

J. Pan, Z. Ye, X. Yang, X. Yang, W. Liu, L. Wang, and J. Bian, “Bpqp: A differentiable convex optimization framework for efficient end-to-end learning,”Advances in Neural Information Processing Systems, vol. 37, pp. 77 468–77 493, 2024

2024
[27]

Differentiation through black-box quadratic programming solvers,

C. Magoon, F. Yang, N. Aigerman, and S. Kovalsky, “Differentiation through black-box quadratic programming solvers,”Advances in Neural Information Processing Systems, vol. 38, pp. 108 486–108 517, 2026

2026
[28]

A. J. Conejo and L. Baringo,Power system operations. Springer, 2018, vol. 14, no. 54

2018
[29]

Deep learning,

Y . LeCun, Y . Bengio, and G. Hinton, “Deep learning,”nature, vol. 521, no. 7553, pp. 436–444, 2015

2015
[30]

Ecos: An socp solver for embedded systems,

A. Domahidi, E. Chu, and S. Boyd, “Ecos: An socp solver for embedded systems,” in2013 European control conference (ECC). IEEE, 2013, pp. 3071–3076

2013
[31]

Distributed optimization and statistical learning via the alternating direction method of multipliers,

P. Neal, C. Eric, P. Borja, and E. Jonathan, “Distributed optimization and statistical learning via the alternating direction method of multipliers,” Foundations and Trends® in Machine learning, vol. 3, no. 1, pp. 1–122, 2011

2011
[32]

Osqp: An operator splitting solver for quadratic programs,

B. Stellato, G. Banjac, P. Goulart, A. Bemporad, and S. Boyd, “Osqp: An operator splitting solver for quadratic programs,”Mathematical Programming Computation, vol. 12, no. 4, pp. 637–672, 2020

2020
[33]

Qpalm: A proximal aug- mented lagrangian method for nonconvex quadratic programs,

B. Hermans, A. Themelis, and P. Patrinos, “Qpalm: A proximal aug- mented lagrangian method for nonconvex quadratic programs,”Mathe- matical Programming Computation, vol. 14, no. 3, pp. 497–541, 2022

2022
[34]

Pytorch: An imperative style, high-performance deep learning library,

A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antigaet al., “Pytorch: An imperative style, high-performance deep learning library,”Advances in neural information processing systems, vol. 32, 2019

2019
[35]

Lsqr: An algorithm for sparse linear equations and sparse least squares,

C. C. Paige and M. A. Saunders, “Lsqr: An algorithm for sparse linear equations and sparse least squares,”ACM Transactions on Mathematical Software (TOMS), vol. 8, no. 1, pp. 43–71, 1982

1982
[36]

Nocedal and S

J. Nocedal and S. J. Wright,Numerical optimization. Springer, 1999

1999
[37]

S. P. Boyd and L. Vandenberghe,Convex optimization. Cambridge university press, 2004

2004
[38]

Solution of sparse indefinite systems of linear equations,

C. C. Paige and M. A. Saunders, “Solution of sparse indefinite systems of linear equations,”SIAM journal on numerical analysis, vol. 12, no. 4, pp. 617–629, 1975

1975
[39]

A synthetic texas power system with time-series weather-dependent spatiotemporal profiles,

J. Lu, X. Li, H. Li, T. Chegini, C. Gamarra, Y . E. Yang, M. Cook, and G. Dillingham, “A synthetic texas power system with time-series weather-dependent spatiotemporal profiles,”Sustainable Energy, Grids and Networks, p. 101774, 2025

2025
[40]

Gurobi Optimizer Reference Manual,

Gurobi Optimization, LLC, “Gurobi Optimizer Reference Manual,”
[2025]

Available: https://www.gurobi.com

[Online]. Available: https://www.gurobi.com

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [1]

Cost-oriented load forecasting,

J. Zhang, Y . Wang, and G. Hug, “Cost-oriented load forecasting,” Electric Power Systems Research, vol. 205, p. 107723, 2022

work page 2022

[2] [2]

Prescribing net demand for two-stage electricity generation scheduling,

J. M. Morales, M. Munoz, and S. Pineda, “Prescribing net demand for two-stage electricity generation scheduling,”Operations Research Perspectives, vol. 10, p. 100268, 2023

work page 2023

[3] [3]

Decision-focused learning for power system decision-making under uncertainty,

H. Zhang, R. Li, Q. Du, J. Tao, S. Pineda, G. Kariniotakis, S. Camal, C. B. Monroc, M. Sun, C. Wan, W. Xu, and F. Teng, “Decision-focused learning for power system decision-making under uncertainty,”IEEE Transactions on Power Systems, vol. 41, no. 1, pp. 307–323, 2026

2026

[4] [4]

Learning-augmented power system operations: A unified optimization view,

W. Xu, Z. Chu, and F. Teng, “Learning-augmented power system operations: A unified optimization view,” 2026. [Online]. Available: https://arxiv.org/abs/2505.05203

arXiv 2026

[5] [5]

Feature-driven economic improvement for network-constrained unit commitment: A closed-loop predict-and-optimize framework,

X. Chen, Y . Yang, Y . Liu, and L. Wu, “Feature-driven economic improvement for network-constrained unit commitment: A closed-loop predict-and-optimize framework,”IEEE Transactions on Power Systems, vol. 37, no. 4, pp. 3104–3118, 2022

2022

[6] [6]

Towards improving unit commitment economics: An add-on tailor for renewable energy and reserve predic- tions,

X. Chen, Y . Liu, and L. Wu, “Towards improving unit commitment economics: An add-on tailor for renewable energy and reserve predic- tions,”IEEE Transactions on Sustainable Energy, vol. 15, no. 4, pp. 2547–2566, 2024

work page 2024

[7] [7]

Task-based end-to-end model learning in stochastic optimization,

P. Donti, B. Amos, and J. Z. Kolter, “Task-based end-to-end model learning in stochastic optimization,”Advances in neural information processing systems, vol. 30, 2017

2017

[8] [8]

A task-based day-ahead load forecasting model for stochastic economic dispatch,

J. Han, L. Yan, and Z. Li, “A task-based day-ahead load forecasting model for stochastic economic dispatch,”IEEE Transactions on Power Systems, vol. 36, no. 6, pp. 5294–5304, 2021

work page 2021