Decision-Focused Scenario Generation and Selection for Efficient and Robust Grid Dispatch

Thomas Morstyn; Yangze Zhou; Yihong Zhou; Yi Wang

REVIEW 3 major objections 8 minor 34 references

Decision-Focused Scenario Generation and Selection for Efficient and Robust Grid Dispatch

T0 review · 3 major / 8 minor · reviewed 2026-07-08 · glm-5.2

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Pith's one-line read Train scenarios on grid cost, not forecast error: 0.8–2% savings

desk verdict Unified decision-focused scenario generation for DRO dispatch: real framework, selectively reported results read the letter →

arxiv 2607.05830 v1 pith:3KABIUPZ submitted 2026-07-07 cs.LG cs.AI

Yangze Zhou , Yihong Zhou , Thomas Morstyn , Yi Wang This is my paper · ORCID

classification cs.LGcs.AI

keywords decision-focusedlearningscenariogenerationdistributionallyrobustoptimizationpowersystemdispatchgenerativemodelsselectionWassersteinambiguitysetKKTdifferentiation

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 argues that the scenarios fed into distributionally robust optimization (DRO) for power grid dispatch should be trained to minimize downstream operational cost, not statistical forecasting error. The authors build a unified framework that wraps three major generative model families—variational autoencoders (VAEs), generative adversarial networks (GANs), and diffusion models—into a single decision-focused training loop. The key mechanism is a differentiable pipeline: scenarios are generated from a learned joint distribution that captures inter-bus correlations, passed through a differentiable scenario selector that reduces the scenario count for tractability, and then fed into a DRO dispatch formulation whose optimal solution is differentiated via its KKT conditions using the OptNet approach. The gradient of the resulting operational cost flows back through the selector and into the generative model, updating its parameters so that future scenarios are more decision-relevant. The paper demonstrates that this approach reduces operational cost by 0.80%–2.02% across all three generative model types compared to accuracy-oriented training, and that the learned scenario selector consistently outperforms statistical clustering methods like K-means and hierarchical clustering.

What carries the argument

The framework has three mechanical components. First, a generative model (VAE decoder, GAN generator, or diffusion denoising network) produces a pool of jointly correlated scenarios from a shared latent space. Second, a differentiable scenario selector parameterized by a neural network outputs soft selection weights via Gumbel-Softmax reparameterization, constructing a reduced scenario set as convex combinations of pool scenarios during training and performing hard discrete selection at evaluation. Third, the DRO dispatch problem is reformulated as a linear program whose KKT conditions are differentiated using OptNet, yielding the sensitivity of the optimal dispatch cost to the inputscenario

What would settle it

If the DRO dispatch LP frequently encounters degenerate vertices (where the KKT Jacobian is singular), the gradient computation in Equation 16 becomes invalid, and the decision-focused training signal is corrupted. One could test this by tracking the condition number of the KKT Jacobian across training iterations on realistic grid data and checking whether degenerate points arise often enough to destabilize training.

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Extended reading notes

Core claim

The central discovery is that a single decision-focused training protocol can be applied across architecturally distinct generative models (VAE, GAN, diffusion) for scenario generation in DRO-based grid dispatch, by abstracting each model into a common forward interface and routing the operational-cost gradient back through model-specific backward paths. The protocol works because the DRO dispatch problem, when reformulated as a linear program, admits differentiation through its KKT conditions, creating a valid gradient path from dispatch cost to generative model parameters. A secondary discovery is that a learned, differentiable scenario selector trained under the same cost objective can be

Load-bearing premise

The gradient computation that enables the entire decision-focused training loop assumes that the DRO dispatch linear program has a locally unique KKT point and that the Jacobian of the KKT system is nonsingular at the optimum. The paper states this assumption but does not verify it for the specific dispatch formulation used, and degenerate LP vertices—where multiple constraints bind simultaneously—are common in power system dispatch problems and would make the Jacobian sing

Editorial extensions

If this is right

Power system operators could adopt decision-focused scenario generation as a drop-in replacement for accuracy-oriented forecasting pipelines, obtaining dispatch decisions that directly account for the asymmetric cost structure of over- vs. under-forecasting.
The model-agnostic design means that as new generative architectures emerge (e.g., flow matching, transformer-based generators), they can be integrated into the same decision-focused training loop without redesigning the differentiation pipeline.
The differentiable scenario selector could be applied to other computationally expensive optimization problems beyond grid dispatch, such as supply chain or portfolio optimization, where scenario reduction is needed but statistical similarity does not capture decision relevance.
Joint distribution modeling across buses eliminates physically implausible scenario combinations, potentially improving grid reliability metrics that are not captured by cost alone.

Reading between the lines

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

The 0.80%–2.02% cost reduction is measured on a single 14-bus system with loads from one region of China. Whether the relative benefit scales to larger transmission networks with hundreds of buses and more complex topology remains an open question—the computational cost of the KKT-based backward pass grows with problem size, and the benefit may be diluted or amplified in larger systems.
The framework's success hinges on the DRO dispatch LP having a locally unique KKT point with a nonsingular Jacobian. Power system dispatch problems frequently encounter degenerate LP vertices where multiple constraints bind simultaneously, which would corrupt the gradient signal. The paper does not report how often this occurs in practice or how the training behaves when it does.
The truncated backpropagation strategy for diffusion models (keeping only the last n_tru denoising steps) introduces an approximation whose quality likely depends on the variance schedule and the value of n_tru. The trade-off between gradient fidelity and memory cost is not fully characterized, and the optimal truncation depth may vary with the complexity of the uncertainty distribution.

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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

read the letter

Bottom line: this paper does something genuinely useful — it wraps VAE, GAN, and diffusion models into a single decision-focused training pipeline for Wasserstein-DRO grid dispatch, with a differentiable Gumbel-Softmax scenario selector — but the empirical evidence is thinner than the abstract suggests and needs hardening before publication. The code is public, which matters. The framework design is clean: the model-agnostic abstraction over three generative paradigms is legitimate, the OptNet backward pass through the DRO LP is correctly derived, and the correlation analysis (Figs. 7-8) convincingly shows that joint generation captures inter-bus dependence that separate forecasting misses. The scenario selector comparison against K-means, K-medoids, and hierarchical clustering (Table II) is a fair benchmark and the proposed selector wins consistently. That said, two problems stand out. First, the abstract claims 0.80–2.02% cost reduction, but Table I shows four of eight settings at 0.11–0.49%. The abstract is cherry-picking the better results. Second, there are no confidence intervals, no random-seed variation, and no significance tests on the cost comparisons. The 10-run protocol is used only for timing benchmarks, not for the cost numbers that actually matter. For improvements in the 0.1–0.5% range, single-point estimates are not enough. On the KKT nonsingularity concern (Eq. 16): this is a standard assumption in the OptNet literature and the paper cites Amos & Kolter correctly. It would be better to verify it for this specific LP structure, but I would not call it a load-bearing flaw — the OptNet machinery is well-established and the empirical results are consistent with the gradients being computed correctly. The bigger issue is scale: one 14-bus system, one dataset. The generalizability claim across 'mainstream generative models' needs at least one larger test system. The truncated backpropagation for diffusion (n_tru steps) is a reasonable engineering choice but the hyperparameter is not reported. This paper is for researchers working at the intersection of decision-focused learning and power system optimization. It deserves a serious referee who can ask for: (1) honest reporting of the full improvement range, (2) repeated trials with significance tests on Table I, (3) at least one larger system, and (4) reported hyperparameters. The framework is sound enough to warrant the revision cycle.

Referee Report

3 major / 8 minor

Summary. The paper proposes a unified decision-focused scenario generation and selection framework for distributionally robust optimization (DRO)-based power grid dispatch. The framework backpropagates operational cost gradients through the DRO optimization into generative models (VAE, GAN, diffusion), enabling scenario generation that is directly optimized for downstream dispatch cost rather than statistical accuracy. A differentiable scenario selector based on Gumbel-Softmax is introduced to reduce computational burden. Experiments on an IEEE 14-bus system with load data from southern China demonstrate cost reductions compared to accuracy-oriented methods.

Significance. The paper addresses a relevant problem at the intersection of decision-focused learning and power systems optimization. The model-agnostic design across VAE, GAN, and diffusion models is a strength, as is the differentiable scenario selector. The provision of a public code repository (https://github.com/hkuedl/Cost-oriented-Generative-Model) supports reproducibility. The framework is applied to a concrete two-stage Wasserstein-DRO dispatch formulation with tractable reformulation.

major comments (3)

Table I and Abstract: The abstract claims cost reductions of '0.80%–2.02%' across different generative models. However, Table I shows that for several settings (Parametric, Non-parametric, GAN-Separate, Diff-Separate), the DF(Selector)-AO improvements range from 0.11% to 0.49%, well below the stated 0.80% lower bound. The abstract appears to selectively report only the better-performing settings. The authors should either revise the claimed range to reflect all results or explicitly state that the 0.80%–2.02% range applies specifically to the joint forecasting settings.
Table I: No statistical significance testing or random-seed variation is reported for the cost comparisons. The improvements in several settings are below 0.50% (e.g., 0.11% for Parametric with Selector-Inner), which may be within run-to-run variance. The paper mentions 10 runs only for timing benchmarks (§V.D, Fig. 12), not for the cost results. Without confidence intervals or repeated trials, it is unclear whether these small improvements are robust. The authors should provide multi-seed results with standard deviations or significance tests for the main cost comparisons.
§IV.A, Eq. (16): The KKT-based implicit differentiation assumes the Jacobian ∂K/∂x̃ is nonsingular at the optimum. The paper states this assumption but does not verify it for the specific DRO dispatch LP (12). LP degeneracy is common in power-system dispatch problems, and if the Jacobian is singular at degenerate vertices, the gradient computation is invalid. The authors should either provide conditions under which nonsingularity holds for the specific LP structure in (12) or discuss how degeneracy is handled in practice (e.g., via regularization or perturbation).

minor comments (8)

§IV.B, Eq. (22): The smoothing coefficient ν is introduced but its value is not specified in the experimental setup. Please state the value used.
§IV.B, Eq. (23): The Gumbel-Softmax temperature τ_g is mentioned but its annealing schedule or final value is not provided. Please specify.
§IV.A, diffusion model backward propagation: The truncated backpropagation strategy uses n_tru steps, but the value of n_tru is not stated. Please include this in the experimental setup.
§V.A: The values of hyperparameters ε (ambiguity set radius), K (number of selected scenarios), and λ (regularization weight) are not clearly tabulated. A table summarizing all hyperparameter values would improve reproducibility.
Table I: The row label 'DF(Selector)-AO(Random)' is ambiguous. It is unclear whether this represents the best selector result minus AO, or a specific selector variant. Clarification is needed.
§V.C, Fig. 9: The x-axis values span 10^1 to 10^4, but the tick labels are not shown clearly. Please improve the readability of the axis labels.
§V.A: Only a single 14-bus system with one dataset is tested. While the authors mention the framework is applicable to other systems, testing on at least one additional system (e.g., IEEE 30-bus or 118-bus) would strengthen the generalizability claim.
The paper would benefit from a brief discussion of the computational overhead introduced by the OptNet backward pass relative to the forward solve, particularly for the full (non-simplified) system.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful review and constructive feedback. The referee raises three major points: (1) the abstract's cost-reduction range appears to selectively report only better-performing settings; (2) no statistical significance testing or multi-seed variation is reported for the main cost comparisons; and (3) the KKT-based implicit differentiation assumes nonsingularity of the Jacobian, which may fail under LP degeneracy. We address each point below and commit to revisions where appropriate.

read point-by-point responses

Referee: Table I and Abstract: The abstract claims cost reductions of '0.80%–2.02%' across different generative models. However, Table I shows that for several settings (Parametric, Non-parametric, GAN-Separate, Diff-Separate), the DF(Selector)-AO improvements range from 0.11% to 0.49%, well below the stated 0.80% lower bound. The abstract appears to selectively report only the better-performing settings. The authors should either revise the claimed range to reflect all results or explicitly state that the 0.80%–2.02% range applies specifically to the joint forecasting settings.

Authors: The referee is correct that the abstract's stated range of 0.80%–2.02% does not encompass all settings reported in Table I. Examining the table, the improvements for the joint forecasting settings (VAE-Joint, GAN-Joint, Diff-Joint) range from 0.73% to 2.09%, while the separate forecasting and traditional methods show smaller improvements (0.11%–0.49%). The 0.80%–2.02% range was intended to characterize the joint forecasting results, where the decision-focused framework's benefits are most pronounced, but this scope was not made clear in the abstract. We will revise the abstract to explicitly state that the 0.80%–2.02% range applies to the joint forecasting settings, and we will also report the full range of improvements across all settings to avoid any impression of selective reporting. revision: yes
Referee: Table I: No statistical significance testing or random-seed variation is reported for the cost comparisons. The improvements in several settings are below 0.50% (e.g., 0.11% for Parametric with Selector-Inner), which may be within run-to-run variance. The paper mentions 10 runs only for timing benchmarks (§V.D, Fig. 12), not for the cost results. Without confidence intervals or repeated trials, it is unclear whether these small improvements are robust. The authors should provide multi-seed results with standard deviations or significance tests for the main cost comparisons.

Authors: The referee raises a valid concern. We acknowledge that the cost results in Table I are reported as single-run values without confidence intervals or standard deviations, while the timing benchmarks in §V.D do use 10 runs. This is an inconsistency in our experimental reporting. We will conduct multi-seed experiments (at least 5–10 runs with different random seeds) for the main cost comparisons in Table I and report standard deviations. For settings where improvements are below 0.50%, we will explicitly discuss whether the differences are statistically significant. We note that for the joint forecasting settings where improvements exceed 0.73%, we expect these to be robust, but we will verify this empirically. We agree this is necessary for the reader to assess the reliability of the reported improvements. revision: yes
Referee: §IV.A, Eq. (16): The KKT-based implicit differentiation assumes the Jacobian ∂K/∂x̃ is nonsingular at the optimum. The paper states this assumption but does not verify it for the specific DRO dispatch LP (12). LP degeneracy is common in power-system dispatch problems, and if the Jacobian is singular at degenerate vertices, the gradient computation is invalid. The authors should either provide conditions under which nonsingularity holds for the specific LP structure in (12) or discuss how degeneracy is handled in practice (e.g., via regularization or perturbation).

Authors: The referee correctly identifies a technical gap. The nonsingularity of ∂K/∂x̃ at the KKT point is equivalent to the standard second-order sufficient condition (SOSC) for the LP, which requires linear independence of active constraints (LICQ) and strict complementarity. We acknowledge that LP degeneracy, where strict complementarity fails, is common in power-system dispatch problems and can arise in our formulation (12) when, for example, multiple generators hit their capacity limits simultaneously or when reserve constraints are binding at the same time step. We do not currently verify or handle this condition in practice. In the revised manuscript, we will add a discussion of this issue, including: (1) the specific conditions under which nonsingularity holds for the LP structure in (12), (2) a note that in our experiments we did not encounter numerical issues, which suggests degeneracy did not arise in the tested instances, and (3) a practical mitigation strategy such as adding a small quadratic regularization term to the LP objective or applying a perturbation to ensure strict complementarity. We note that such regularization is standard in the differentiable optimization literature (e.g., OptNet-based approaches). However, we cannot at this stage provide a formal proof that nonsingularity always holds for the specific DRO dispatch LP, so the discussion will be framed as conditions and practical mitigations rather than a guarantee. revision: partial

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity; one minor non-load-bearing self-citation.

full rationale

The paper's core derivation chain is self-contained. The decision-focused objective (Eq. 1) is a standard predict-and-optimize formulation, not self-definitional. The KKT-based implicit differentiation (Eq. 16) relies on OptNet [28] (Amos & Kolter, an external, widely-used reference) and the implicit function theorem — standard machinery, not a self-citation. The Wasserstein DRO reformulation (Eq. 12) relies on [27] (Skalyga et al., external). The only self-citation is [21] (Zhou, Morstyn), cited merely for the general observation that DRO optimization is computationally expensive — this is not load-bearing for any derivation or central claim. The empirical evaluation in Table I measures cost reductions against accuracy-oriented baselines on held-out 2023 test data, so the 'prediction' is not statistically forced by the training objective. The scenario selector is trained and evaluated on the same decision-focused cost, but this is by design (it selects decision-relevant scenarios) and is evaluated out-of-sample, so it is not circular. The selective reporting concern (abstract claims 0.80%–2.02% but Table I shows 0.11%–2.09%) is a validity/statistical issue, not a circularity issue. Score 1 reflects the minor, non-load-bearing self-citation [21].

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

The paper introduces no new physical entities, particles, forces, or dimensions. The scenario selector network is a new architectural component but is a standard neural network, not a postulated physical object. The free parameters are hyperparameters of the training pipeline rather than physically fitted constants. The key axioms are standard for the power-systems DRO literature except for the unverified KKT nonsingularity and the ad-hoc diffusion truncation.

free parameters (6)

ε (ambiguity set radius) = selected via validation dataset
Controls the Wasserstein ambiguity set size; selected on validation data per Section V.A but selection procedure not detailed.
K (number of selected scenarios) = varied (10–190 in experiments)
Determines reduced scenario set size; chosen experimentally.
λ (regularization weight) = not specified
Weights the diversity regularizer in selector training (L = C* + λL_reg); value not reported.
ν (smoothing coefficient) = not specified
Controls uniform smoothing in selection distribution (Eq. 22); value not reported.
τ_g (Gumbel-Softmax temperature) = not specified
Controls softness of discrete selection approximation (Eq. 23); annealing schedule not reported.
n_tru (truncated backprop steps for diffusion) = not specified
Number of final denoising steps retained for gradient computation; value not reported.

assumptions (5)

domain assumption KKT Jacobian nonsingularity: ∂K/∂x̃ is nonsingular at the optimum (Eq. 16)
Section IV.A: required for implicit differentiation to compute gradients through the DRO optimization layer. Not verified for the specific LP structure of Eq. 12.
domain assumption DC power-flow approximation is valid for the test system
Section III.A, Eq. 2h: line flows modeled as linear in voltage angle differences. Standard for transmission-level dispatch but limits applicability to distribution networks.
standard math Recourse value function Q(x,y) is convex in y
Section IV.A: stated because the second-stage problem is an LP in u with y entering linearly. This is a standard result for LP recourse.
ad hoc to paper Truncated backpropagation through final n_tru diffusion steps preserves sufficient gradient signal
Section IV.A: adopted to address memory and gradient attenuation but no sensitivity analysis or justification for the truncation choice is provided.
domain assumption The two-stage dispatch model (adapted from [26]) is representative of real-world DRO dispatch
Section III.A: the framework is instantiated on this specific model; generalization to other dispatch structures is claimed but not demonstrated.

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Cite this review

Pith. "Pith review of Decision-Focused Scenario Generation and Selection for Efficient and Robust Grid Dispatch." pith.science (2026). https://pith.science/paper/3KABIUPZ

@misc{pith2026260705830,
  author       = {Pith},
  title        = {Pith review of: Decision-Focused Scenario Generation and Selection for Efficient and Robust Grid Dispatch},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3KABIUPZ}},
  note         = {Machine review of arXiv:2607.05830}
}

read the original abstract

The increasing uncertainty from flexible demand and renewable generation has made distributionally robust optimization (DRO) an important tool for robust power system dispatch. DRO relies on forecast scenarios to construct ambiguity sets, but conventional scenario generation pipelines are often trained in an accuracy-oriented manner and may neglect spatial correlations among uncertainties. This mismatch can produce ambiguity sets that are statistically plausible but suboptimal for downstream operation. This work proposes a decision-focused generative framework for correlated scenario generation in DRO-based dispatch. Instead of training generative models solely to fit the historical uncertainty distribution, the proposed framework optimizes generated scenarios according to their induced downstream operational cost. The proposed framework is tailored to mainstream generative models, including variational autoencoders, generative adversarial networks, and diffusion models, while capturing the joint distribution of uncertainties across buses. To improve computational tractability, we further develop a differentiable scenario selector that selects decision-relevant scenarios from a generated pool and can be trained within the same decision-focused pipeline. Case studies demonstrate that the proposed framework effectively reduces 0.80%-2.02% operational cost across different generative models compared to accuracy-oriented methods.

Figures

Figures reproduced from arXiv: 2607.05830 by the authors.

**Figure 1.** Overview of the proposed decision-focused scenario generation framework and its interaction with downstream dispatch. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗

**Figure 2.** Simplified illustration of the proposed decision-focused scenario [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** The framework of the proposed scenario selector [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (7 more)

**Figure 4.** Figure 4: Accuracy comparison between the generative approach and parametric [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: Accuracy comparison between the generative approach and non [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

**Figure 7.** Figure 7: Correlation between different nodes learned by different generative [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

**Figure 9.** Figure 9: It can be seen that, for all radii, the joint forecasting ap [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]

**Figure 6.** Figure 6: The accuracy comparison of separate forecasting and joint forecasting [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

**Figure 10.** Figure 10: The average costs of AO, DF, and DF(Selector) methods for the [PITH_FULL_IMAGE:figures/full_fig_p009_10.png]

**Figure 12.** Figure 12: The forward and backward time per sample for VAE in the joint [PITH_FULL_IMAGE:figures/full_fig_p010_12.png]

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Pith tools

Reviewed July 8, 2026 · model on record in the stance chip above.

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