A Predict-then-Schedule framework for Power Distribution Networks with AI Data Centers

Jiebao Zhang; Juan Huang; Siqi Yan; Xi Yao; Ye Shi

REVIEW 4 major objections 3 minor 18 references

This paper proposes an end-to-end Predict-then-Schedule framework that trains the workload predictor through the downstream scheduling optimization, so the model learns forecasts that reduce operational cost and grid violations rather than

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2026-08-01 17:44 UTC pith:DSURGDYW

load-bearing objection Useful decision-focused learning application with a genuine reproducibility gap in the workload-capacity scaling. the 4 major comments →

arxiv 2607.17514 v1 pith:DSURGDYW submitted 2026-07-20 cs.CE

A Predict-then-Schedule framework for Power Distribution Networks with AI Data Centers

Siqi Yan , Jiebao Zhang , Xi Yao , Juan Huang , Ye Shi This is my paper

classification cs.CE

keywords predict-then-optimizedecision-focused learningAI data centerworkload schedulingpower distribution networkdifferentiable convex optimizationload sheddingimplicit differentiation

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper argues that for AI data center workloads that can be shifted in time and space, training the upstream predictor to minimize the downstream scheduling cost—rather than forecast error—yields schedules that are cheaper and safer. It builds a three-layer pipeline: an LSTM predictor, a differentiable convex optimization layer that solves the grid-constrained scheduling problem, and an evaluation layer that penalizes load shedding via an over-shifted loss. On a modified IEEE 33-bus system, the approach reports a substantial reduction in operational cost and near-zero constraint violations, while deliberately accepting higher mean squared error. The point is that statistical accuracy is not the right objective when predictions feed an optimizer; decision quality is what matters. If true, this supports decision-focused learning for grid-coordinated data center operations.

Core claim

The central claim is that end-to-end decision-focused training is superior to the conventional two-stage pipeline for coordinating delay-tolerant AI workloads with distribution network constraints. The framework treats the convex scheduling problem as a differentiable layer using implicit differentiation through the KKT system, so the gradient of an over-shifted loss—which combines generation cost and a quadratic penalty for load shedding—can be backpropagated into the predictor. The learned forecasts intentionally deviate from ground truth, over-forecasting at some hours and under-forecasting at others, to steer the optimizer away from infeasible, high-cost decisions. With penalty coefficie

What carries the argument

The key mechanism is the differentiable convex optimization layer: the downstream scheduling problem is written in compact form with objective J(y,ϕ), linear equalities and inequalities, and its KKT conditions are differentiated implicitly to obtain dy*/dϕ. This lets the gradient of the over-shifted loss L_cost flow back through the optimizer into the prediction network parameters θ. The over-shifted loss itself is the second load-bearing piece: it relaxes the hard capacity constraint with a load-shedding variable P_shed and adds a quadratic penalty γ(P_shed)^2, so the evaluation problem remains feasible and gradients stay continuous while the model is incentivized to hedge against violation

Load-bearing premise

The load-bearing premise is that the workload data, normalized to [0,1], can be fed into a scheduling model whose full capacity is 0.15 units; without an unstated rescaling, the optimization would be infeasible, so the reported cost and violation comparison rests on that hidden unit mapping.

What would settle it

Rerun the experiments with explicit physical units and a stated peak-workload-to-capacity ratio, and check whether PTS still beats the two-stage baseline and still learns to over- and under-forecast; if the advantage vanishes or the learned distortion reverses, the central claim depends on the unstated rescaling.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

Because the predictor is trained through the optimizer, the model learns to hedge: it deliberately distorts forecasts (over-forecasting at low-price hours, under-forecasting at peak) to avoid infeasible schedules.
The over-shifted loss with a sufficiently large γ drives violations to near zero; both γ=10 and γ=100 converge to similar cost levels, so the framework is robust to the penalty magnitude.
A fixed 80% capacity reserve reduces violations but is suboptimal in cost compared to learned hedging, implying that decision-aware training can replace static safety margins.
Because the downstream problem remains an exact convex program, the scheduling decisions stay interpretable while training end-to-end.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The reported unit mismatch—workload normalized to [0,1] versus a datacenter capacity of 0.15 units—suggests the comparison depends on an unstated rescaling of the workload data; if the data were not rescaled, the scheduling problem would be infeasible without massive shedding, so the learned hedging behavior may be partly an artifact of that scaling choice.
A natural testable extension is to rerun the comparison with a two-stage baseline that uses an optimized safety margin rather than a fixed 80% reserve; the advantage of PTS might shrink or disappear under that stronger baseline.
The implicit differentiation assumes LICQ and strict complementarity; in degenerate cases such as load shedding at zero or binding bounds, the gradient estimates may be biased, so robustness to degeneracy is worth probing.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

Useful decision-focused learning application with a genuine reproducibility gap in the workload-capacity scaling.

read the letter

Quick read of arXiv:2607.17514. The paper takes the standard predict-then-optimize machinery (Donti, Elmachtoub, Amos, Agrawal) and applies it to coordinating AI data center workload scheduling with a distribution grid. That's a timely and sensible thing to do, and the authors get the core mechanism right: train the forecaster against the downstream scheduling loss, use implicit differentiation through a convex optimization layer, and let the predictor deliberately distort forecasts to avoid constraint violations. The over-shifted loss with a load-shedding penalty is a reasonable way to keep the evaluation problem feasible and differentiable. If I had a student working on data center demand response, I'd point them here.

The math is standard but coherent. The empirical story is the expected one: PTS trades MSE for much lower constraint violations and a lower combined cost-vs-penalty loss than two-stage. The learned over-forecasting during cheap hours and under-forecasting during peak hours is a nice illustration of decision-focused behavior.

The soft spots are real and mostly in the experiments. The biggest one: Section IV says the workload is normalized to [0,1] and the data center capacity P_full is 0.15 units. With Eq. (9) and the conservation constraint (8b), a workload series with a mean above 0.15 will force P_IT above P_full at some hour regardless of scheduling. Since typical normalized load data has a mean well above 0.15, the optimization would be infeasible as written. The authors must have rescaled the workload or softened the constraint; they don't say which, and that rescaling changes the relative weight of generation cost vs shedding penalty in the reported loss. So the Table I numbers are not reproducible or interpretable. Also, 'Cost Loss' includes the load-shedding penalty, not a pure electricity cost, so 'reduces operational cost' is overstated if that's all they report. There are no error bars, no multiple seeds, and no code/data. These are all fixable, but they need to be fixed before the numbers can be taken at face value.

Who is this for? Researchers working on decision-focused learning for power systems or data center-grid coordination. It's a useful case study, not a breakthrough. I'd send it to peer review, but with a clear request for the scaling details, a separate electricity-cost metric, and code/data. The qualitative conclusion is plausible and consistent with prior PTO results, so I wouldn't reject it.

Referee Report

4 major / 3 minor

Summary. The paper proposes an end-to-end Predict-then-Schedule (PTS) framework for coordinating delay-tolerant AI data center workload with distribution network operation. An LSTM workload predictor is trained jointly with a differentiable convex optimization layer that solves a DistFlow-based grid scheduling problem. A decision-focused loss, called the over-shifted loss, combines electricity generation cost with a quadratic penalty on load shedding. Simulations on a modified IEEE 33-bus system with a single data center compare PTS against a conventional two-stage predictor and a reserve-based baseline. The reported results show that PTS achieves much lower cost loss and constraint violations at the expense of higher prediction MSE. The central claim is that end-to-end decision-focused training significantly reduces operational cost and enhances security relative to the conventional two-stage baseline.

Significance. The paper addresses a timely and important problem: coordinating AI data center workload with distribution grid constraints through decision-focused learning. The mathematical framework is standard, and the use of implicit differentiation through a convex optimization layer is appropriate. If the empirical claims were properly supported, the work would offer a useful demonstration that end-to-end training can outperform a two-stage pipeline for this application. The formulation of the decision layer and the evaluation layer is clear, and the idea of an over-shifted loss to penalize load shedding is reasonable. However, the current experimental evidence has major gaps: the workload-capacity scaling is not specified, the reported cost metric mixes a tunable penalty with actual electricity cost, the violation metric is undefined, and no code, data, or error bars are provided. These issues prevent the central claim from being verified as presented.

major comments (4)

[Section IV.A, Eqs. (6)-(9)] The simulation setup is internally inconsistent. In IV.A.1 the data center full power capacity is P_full=0.15 units, while IV.A.2 states the workload is normalized to [0,1]. Equation (9) sets P_IT_i,t = sum_j sum_s \hat w_{j,s} M_{j,i,s,t} + P_idle_i. With one data center and P_idle=0, any hour with \hat w > 0.15 violates the hard capacity constraint (6). The decision layer (10) enforces (6), so the optimization is infeasible for typical normalized workloads unless an unstated rescaling is applied. The paper does not specify any scaling factor between the workload data and the power capacity, nor any relaxation of the decision-layer capacity constraint. Since the relative magnitude of generation cost versus shedding penalty in the over-shifted loss (13) depends directly on this mapping, the numerical results in Table I are not reproducible or interpretable. Please clarify the unit mappin
[Section III-B, Eq. (13), Table I] The over-shifted loss L_cost in Eq. (13a) is the sum of electricity generation cost and a quadratic penalty gamma (P_shed)^2. This penalty has units that do not match the generation cost, and gamma is a user-chosen weight. Table I reports 'Cost Loss' using this composite quantity, so the comparison between PTS and Two-Stage conflates actual operational cost with an arbitrary penalty term. For the Two-Stage baseline, the high cost loss is largely penalty from violations (violation 0.7518), not generation cost. The abstract's claim of 'significantly reduces operational cost' is not substantiated unless the electricity cost and the shedding penalty are reported separately, or the penalty is given a physically motivated monetary interpretation. Please report the pure generation cost component and justify the choice of gamma.
[Section IV.B, Table I, Fig. 3b] The metric 'Violation' appearing in Table I and Fig. 3b is never defined. The text refers to 'magnitude of constraint violations' but gives no formula, units, or aggregation method. Since the security claim rests on the comparison 0.0007 vs 0.7518, the definition is essential. Please specify whether this is total load shedding, the maximum per-bus voltage or capacity violation, an average over the horizon, or another quantity, and provide its units.
[Section IV.A, Table I] The experimental evaluation reports a single run with no error bars, no multiple seeds, and no code or data release. The workload dataset is described as 'synthesized from real-world power demand forecasting data', but the source and preprocessing steps are not given. Given that the central claim is an empirical comparison, the absence of variance information and reproducibility artifacts makes it impossible to assess the statistical significance of the reported differences. Please provide code/data (or a detailed description), report results over multiple seeds, and include confidence intervals or standard deviations.

minor comments (3)

[Eq. (4)] The voltage constraint in Eq. (4) appears to have missing superscript bars: it is written as 'v 2 i ≤V i,t ≤ v2 i ', presumably meaning \underline{v}_i^2 and \overline{v}_i^2. Please correct the typesetting.
[Fig. 4 and Fig. 5] The captions and axis labels of Figures 4 and 5 contain garbled text due to font encoding issues. They should be regenerated so the figure content is legible.
[Section III-B] The statement 'A sufficiently large \gamma prioritizes the elimination of load shedding' is correct but the sensitivity of the results to \gamma is only shown for two values (10 and 100). A brief discussion of how \gamma is chosen in practice would help.

Circularity Check

0 steps flagged

No significant circularity: the PTS pipeline is trained and evaluated on distinct quantities, and the claimed advantage is an empirical optimization outcome.

full rationale

The paper's derivation chain is: an LSTM predictor f(·;θ) outputs ŵ; the decision layer solves the grid-coordinated scheduling problem (10) with ŵ as a parameter and returns M*; the evaluation layer computes the realized IT load P_IT* from the ground-truth w and M* (Eq. 12), and evaluates Lcost (Eq. 13) with a shed penalty; and the gradient dLcost/dθ is obtained by implicit differentiation through the KKT system (Eqs. 16–18). None of these steps defines its output in terms of its target or fits a parameter and renames it a prediction. Lcost is a genuine function of the ground-truth workload and the schedule; the over/under-forecasting behavior described in Sec. IV.B.2 is an emergent consequence of minimizing that loss, not an input to it. The comparison in Table I is therefore an empirical optimization comparison, not a tautology. The only near-tautological aspect is that the reported cost/violation metric coincides with the PTS training objective; this is standard decision-focused learning and does not reduce the derivation to its inputs. There are no load-bearing self-citations: the differentiable-optimization machinery is cited to external works (OptNet, cvxpylayers). A separate correctness issue exists: Sec. IV.A states P_full=0.15 while workloads are normalized to [0,1] and Eq. (9) uses the normalized values directly, which as written can make the decision layer infeasible; this is a scaling/reproducibility concern, not circularity.

Axiom & Free-Parameter Ledger

4 free parameters · 6 axioms · 0 invented entities

The central claim rests on the convex scheduling model being a faithful proxy for real data center-grid operations and on the simulation's scaling being correct. No new physical entity is introduced; the load-shedding variable P_shed is a soft-constraint relaxation within the loss, and the 'over-shifted loss' is a training objective rather than an entity.

free parameters (4)

load-shedding penalty coefficient gamma = gamma = 10 and 100 (Table I, Fig. 3)
Hand-chosen trade-off coefficient in the over-shifted loss (13a) that directly scales the reported Cost Loss and violation penalty. The authors show robustness across two values but give no tuning criterion.
synthetic electricity price profile = sinusoidal transformation, range 0.5-1.0 (IV.A.1)
Price shape is designed by the authors rather than taken from market data; it determines the economic incentive to shift workload and directly affects the cost comparisons.
data center rating and workload scaling = P_full = 0.15, idle = 0.0, workload normalized to [0,1] (IV.A.1-2)
The mapping from normalized workload to per-unit power is not given; as written, Eq. (9) is dimensionally inconsistent with P_full = 0.15. This is the most consequential free choice in the simulation.
PUE R_PUE = not specified
Eq. (7) maps IT load to grid demand via R_PUE but no numeric value is reported; likely assumed 1, an unstated modeling choice.

axioms (6)

domain assumption Linearized DistFlow (branch flow) model adequately represents the distribution network.
Invoked in Section II.A, Eqs. (1)-(5); linearization and voltage-drop approximations are taken from [15] without validation on the modified 33-bus case.
domain assumption All AI workloads are delay-tolerant and fully dispatchable within the 24-hour horizon with perfect conservation (Eq. 8b).
Section II.C; no deferral limits, deadlines, or SLA constraints are modeled, so the scheduler can shift any workload to any later hour.
domain assumption The downstream optimization is convex and satisfies LICQ and strict complementarity, making the KKT matrix nonsingular for implicit differentiation.
Section III.C; these regularity conditions are asserted rather than verified for the specific instances, and linear programs may have non-unique optima.
domain assumption PUE is a fixed known constant (Eq. 7).
Section II.B; no numeric value or time variation is given.
domain assumption The synthetic workload dataset faithfully represents real AI data center workload statistics.
IV.A.2; the dataset is 'synthesized from real-world power demand forecasting data' and normalized to [0,1], with no source citation or realism validation.
domain assumption Electricity price is known exactly at scheduling time.
Eq. (10a) uses deterministic pi_{i,t}; no price forecast error is modeled.

pith-pipeline@v1.3.0-alltime-deepseek · 11512 in / 17393 out tokens · 144128 ms · 2026-08-01T17:44:27.710301+00:00 · methodology

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read the original abstract

The surge of GPU-intensive workloads in artificial intelligence (AI) data centers drives massive energy demands, leading to soaring costs and significant stress on local power distribution networks. Coordinating delay-tolerant workload scheduling with power grid conditions via precise workload prediction can mitigate these issues. However, a critical gap remains in conventional approaches, i.e., minimizing prediction error does not necessarily lead to minimized downstream operational loss. Hence, this paper proposes an end-to-end Predict-Then-Schedule (PTS) framework that integrates upstream workload prediction with downstream scheduling optimization. By leveraging differentiable convex optimization, the PTS framework maps input features directly to optimal scheduling and enables gradient-based training. Furthermore, to respect the data center's capacity, a workload over-shifted loss combining electricity cost with a penalty for load-shedding is introduced to evaluate scheduling quality. Experiments demonstrate that the proposed framework significantly reduces operational cost and enhances system security compared to the conventional two-stage baseline.

Figures

Figures reproduced from arXiv: 2607.17514 by Jiebao Zhang, Juan Huang, Siqi Yan, Xi Yao, Ye Shi.

**Figure 2.** Figure 2: Our Workload Dataset TABLE I: Comparison of metrics among different training methods. Method MSE Loss Cost Loss Violation Two-Stage 0.0106 31.8381 0.7518 Two-Stage (Reserve) 0.0106 14.9977 0.3190 PTS (γ=10) 0.0490 10.7189 0.0007 PTS (γ=100) 0.0931 10.7205 0.0007 3) Models for Comparison: We benchmark our proposed approach against the traditional two-stage baseline, evaluating performance across various me… view at source ↗

**Figure 3.** Figure 3: Performance Comparison of Different Methods [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: Comparison of task transfer results among four meth [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** Figure 5: Heatmaps of learned transfer matrices Md,c,s,t among four methods. 6, 17-23 and under-forecasting during hours 11-16. This sacrifice in statistical accuracy is not a flaw, but rather a learned strategy, as the PTS models recognize this distorted prediction is essential for guiding the downstream optimization process away from infeasible or high-cost decisions. 3) Impact on Scheduling Decisions: The differe… view at source ↗

discussion (0)

Reference graph

Works this paper leans on

18 extracted references · 1 linked inside Pith

[1]

Recalibrating global data center energy-use estimates,

E. Masanet, A. Shehabi, N. Lei, S. Smith, and J. Koomey, “Recalibrating global data center energy-use estimates,”Science, vol. 367, no. 6481, pp. 984–986, 2020

2020
[2]

Energy and policy con- siderations for deep learning in nlp,

E. Strubell, A. Ganesh, and A. McCallum, “Energy and policy con- siderations for deep learning in nlp,” inProceedings of the 57th annual meeting of the association for computational linguistics, 2019, pp. 3645– 3650

2019
[3]

Data center power system stability—part i: Power supply impedance modeling,

J. Sun, M. Xu, M. Cespedes, and M. Kauffman, “Data center power system stability—part i: Power supply impedance modeling,”CSEE Journal of Power and Energy Systems, vol. 8, no. 2, pp. 403–419, 2022

2022
[4]

Risk-aware energy scheduling for edge computing with microgrid: A multi-agent deep reinforcement learning approach,

M. S. Munir, S. F. Abedin, N. H. Tran, Z. Han, E.-N. Huh, and C. S. Hong, “Risk-aware energy scheduling for edge computing with microgrid: A multi-agent deep reinforcement learning approach,”IEEE Transactions on Network and Service Management, vol. 18, no. 3, pp. 3476–3497, 2021

2021
[5]

Electricity demand and grid impacts of ai data centers: Challenges and prospects,

X. Chen, X. Wang, A. Colacelli, M. Lee, and L. Xie, “Electricity demand and grid impacts of ai data centers: Challenges and prospects,”
[6]

Toward optimal operation of internet data center microgrid,

J. Li and W. Qi, “Toward optimal operation of internet data center microgrid,”IEEE Transactions on Smart Grid, vol. 9, no. 2, pp. 971– 979, 2016

2016
[7]

Safari, K

A. Safari, K. Taghizad-Tavana, and M. Tarafdar Hagh, “Artificial intelligence-driven optimization of internet data center energy consump- tion in active distribution networks: a transformer-based robust control model with spatio-temporal flexibility analytics,”Available at SSRN 5056252, 2024

2024
[8]

Towards accurate prediction for high-dimensional and highly-variable cloud workloads with deep learning,

Z. Chen, J. Hu, G. Min, A. Y . Zomaya, and T. El-Ghazawi, “Towards accurate prediction for high-dimensional and highly-variable cloud workloads with deep learning,”IEEE Transactions on Parallel and Distributed Systems, vol. 31, no. 4, pp. 923–934, 2019

2019
[9]

A review of machine learning-based photovoltaic output power forecasting: Nordic context,

B. D. Dimd, S. V ¨oller, U. Cali, and O.-M. Midtg ˚ard, “A review of machine learning-based photovoltaic output power forecasting: Nordic context,”IEEE Access, vol. 10, pp. 26 404–26 425, 2022

2022
[10]

The cost of photovoltaic forecasting errors in microgrid control with peak pricing,

T. Schmitt, T. Rodemann, and J. Adamy, “The cost of photovoltaic forecasting errors in microgrid control with peak pricing,”Energies, vol. 14, no. 9, p. 2569, 2021

2021
[11]

Smart “predict, then optimize

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

2022
[12]

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
[13]

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,” pp. 1–18
[14]

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
[15]

Branch flow model: Relaxations and convexification—part i,

M. Farivar and S. H. Low, “Branch flow model: Relaxations and convexification—part i,”IEEE Transactions on Power Systems, vol. 28, no. 3, pp. 2554–2564, 2013

2013
[16]

Optnet: Differentiable optimization as a layer in neural networks,

B. Amos and J. Z. Kolter, “Optnet: Differentiable optimization as a layer in neural networks,” inInternational conference on machine learning, 2017, pp. 136–145

2017
[17]

Differentiable convex optimization layers,

A. Agrawal, B. Amos, S. Barratt, S. Boyd, S. Diamond, and J. Z. Kolter, “Differentiable convex optimization layers,”Advances in neural information processing systems, vol. 32, 2019

2019
[2025]

Available: https://arxiv.org/abs/2509.07218

[Online]. Available: https://arxiv.org/abs/2509.07218

Pith/arXiv arXiv

[1] [1]

Recalibrating global data center energy-use estimates,

E. Masanet, A. Shehabi, N. Lei, S. Smith, and J. Koomey, “Recalibrating global data center energy-use estimates,”Science, vol. 367, no. 6481, pp. 984–986, 2020

2020

[2] [2]

Energy and policy con- siderations for deep learning in nlp,

E. Strubell, A. Ganesh, and A. McCallum, “Energy and policy con- siderations for deep learning in nlp,” inProceedings of the 57th annual meeting of the association for computational linguistics, 2019, pp. 3645– 3650

2019

[3] [3]

Data center power system stability—part i: Power supply impedance modeling,

J. Sun, M. Xu, M. Cespedes, and M. Kauffman, “Data center power system stability—part i: Power supply impedance modeling,”CSEE Journal of Power and Energy Systems, vol. 8, no. 2, pp. 403–419, 2022

2022

[4] [4]

Risk-aware energy scheduling for edge computing with microgrid: A multi-agent deep reinforcement learning approach,

M. S. Munir, S. F. Abedin, N. H. Tran, Z. Han, E.-N. Huh, and C. S. Hong, “Risk-aware energy scheduling for edge computing with microgrid: A multi-agent deep reinforcement learning approach,”IEEE Transactions on Network and Service Management, vol. 18, no. 3, pp. 3476–3497, 2021

2021

[5] [5]

Electricity demand and grid impacts of ai data centers: Challenges and prospects,

X. Chen, X. Wang, A. Colacelli, M. Lee, and L. Xie, “Electricity demand and grid impacts of ai data centers: Challenges and prospects,”

[6] [6]

Toward optimal operation of internet data center microgrid,

J. Li and W. Qi, “Toward optimal operation of internet data center microgrid,”IEEE Transactions on Smart Grid, vol. 9, no. 2, pp. 971– 979, 2016

2016

[7] [7]

Safari, K

A. Safari, K. Taghizad-Tavana, and M. Tarafdar Hagh, “Artificial intelligence-driven optimization of internet data center energy consump- tion in active distribution networks: a transformer-based robust control model with spatio-temporal flexibility analytics,”Available at SSRN 5056252, 2024

2024

[8] [8]

Towards accurate prediction for high-dimensional and highly-variable cloud workloads with deep learning,

Z. Chen, J. Hu, G. Min, A. Y . Zomaya, and T. El-Ghazawi, “Towards accurate prediction for high-dimensional and highly-variable cloud workloads with deep learning,”IEEE Transactions on Parallel and Distributed Systems, vol. 31, no. 4, pp. 923–934, 2019

2019

[9] [9]

A review of machine learning-based photovoltaic output power forecasting: Nordic context,

B. D. Dimd, S. V ¨oller, U. Cali, and O.-M. Midtg ˚ard, “A review of machine learning-based photovoltaic output power forecasting: Nordic context,”IEEE Access, vol. 10, pp. 26 404–26 425, 2022

2022

[10] [10]

The cost of photovoltaic forecasting errors in microgrid control with peak pricing,

T. Schmitt, T. Rodemann, and J. Adamy, “The cost of photovoltaic forecasting errors in microgrid control with peak pricing,”Energies, vol. 14, no. 9, p. 2569, 2021

2021

[11] [11]

Smart “predict, then optimize

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

2022

[12] [12]

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

[13] [13]

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,” pp. 1–18

[14] [14]

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

[15] [15]

Branch flow model: Relaxations and convexification—part i,

M. Farivar and S. H. Low, “Branch flow model: Relaxations and convexification—part i,”IEEE Transactions on Power Systems, vol. 28, no. 3, pp. 2554–2564, 2013

2013

[16] [16]

Optnet: Differentiable optimization as a layer in neural networks,

B. Amos and J. Z. Kolter, “Optnet: Differentiable optimization as a layer in neural networks,” inInternational conference on machine learning, 2017, pp. 136–145

2017

[17] [17]

Differentiable convex optimization layers,

A. Agrawal, B. Amos, S. Barratt, S. Boyd, S. Diamond, and J. Z. Kolter, “Differentiable convex optimization layers,”Advances in neural information processing systems, vol. 32, 2019

2019

[18] [2025]

Available: https://arxiv.org/abs/2509.07218

[Online]. Available: https://arxiv.org/abs/2509.07218

Pith/arXiv arXiv