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arxiv: 2606.25362 · v1 · pith:NEPLRDZHnew · submitted 2026-06-24 · 🧮 math.OC · cs.LG

Learning Optimization Proxies for Sequential Contextual Stochastic Programs: An Order Fulfillment Application

Tinghan Ye , Shuaicheng Tong , Changkun Guan , Beste Basciftci , Pascal Van Hentenryck This is my paper

Pith reviewed 2026-06-25 21:18 UTC · model grok-4.3

classification 🧮 math.OC cs.LG
keywords optimization proxycontextual stochastic programmingorder fulfillmentneural networkscenario average approximationsequential decisionsfeasibility enforcement
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The pith

A neural network trained on solver labels approximates solutions to sequential stochastic fulfillment decisions, replacing slow per-epoch optimization with a fast forward pass.

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

The paper establishes that a scenario-embedded neural network can learn to mimic high-quality solutions from a contextual sample average approximation of a two-stage stochastic program for order fulfillment. Each arriving order triggers an assignment to distribution centers and carriers under uncertain delivery times and future demand, and the network produces these assignments after offline training on solver outputs. A decoder then enforces feasibility on the network outputs. If the approach holds, it allows real-time decisions at the speed demanded by peak operations while matching or exceeding the quality of methods that solve the full program online. The demonstration uses a simulator calibrated on actual transaction records to show concrete gains in speed and cost.

Core claim

The central claim is that a learning-based optimization proxy consisting of a scenario-embedded neural network trained offline on C-SAA labels, paired with a feasibility decoder, can replace the per-epoch solve of a two-stage contextual stochastic program for omnichannel order fulfillment. On data from a calibrated simulator, the proxy delivers decisions in a single forward pass that achieve lower realized fulfillment costs than the online C-SAA reference while satisfying the sub-second response requirement.

What carries the argument

Scenario-embedded neural network trained with a composite loss of label imitation, constraint-violation penalty, and self-supervised cost alignment, paired with a decoder that enforces feasibility.

If this is right

  • Decision latency drops by roughly 2800 times compared with solving the finite-sample C-SAA online at each epoch.
  • Realized fulfillment cost improves by 3.3 percent over the online C-SAA reference.
  • Total realized cost falls by at least 10.7 percent relative to established fulfillment policies.
  • Late-delivery rate is reduced by roughly half compared with those policies.

Where Pith is reading between the lines

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

  • The same proxy architecture could be applied to other sequential contextual stochastic programs in logistics or resource allocation if an accurate simulator for label generation is available.
  • Periodic retraining on fresh simulator data would likely be needed if underlying demand or delivery distributions change over time.
  • Direct deployment would require an additional layer of safety checks or fallback solves to handle any residual generalization failures on live data.
  • The approach illustrates how imitation of offline optimization can trade a modest amount of solution quality for orders-of-magnitude gains in decision speed.

Load-bearing premise

The neural network trained offline on C-SAA labels from the calibrated simulator will generalize to produce high-quality feasible decisions on new unseen order sequences without substantial degradation from distribution shift or simulator-reality mismatch.

What would settle it

Collect a set of real operational order sequences, solve the C-SAA online on each to obtain reference decisions and costs, run the trained proxy on the same sequences, and check whether the proxy's realized costs exceed the reference by more than a few percent or produce frequent infeasible assignments.

Figures

Figures reproduced from arXiv: 2606.25362 by Beste Basciftci, Changkun Guan, Pascal Van Hentenryck, Shuaicheng Tong, Tinghan Ye.

Figure 1
Figure 1. Figure 1: Schematic of the optimization proxy for omnichannel order fulfillment. [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Schematic of optimization proxy architecture, training loss, and inference. [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Forward pass of the optimization proxy 𝑓𝜃 . candidates 𝑗 so the embedding size is independent of |J |: eglobal = 𝜙ord (Xord), edc, 𝑗 = 𝜙dc (Xdc, 𝑗), 𝑗 ∈ J. Scenario module. The sampled scenario sets 𝛀dem and 𝛀time are unordered and may vary in size at deployment. For the current product line, identify 𝛀dem = {𝐷 𝜔} 𝐸 𝜔=1 as the scalar demand scenarios and 𝛀time = {𝚫𝜔} 𝐸 𝜔=1 as the deviation matrices 𝚫𝜔 = (Δ… view at source ↗
Figure 4
Figure 4. Figure 4: Optimization model for training the proxy [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Total realized fulfillment cost by evaluation date, summed over orders served each day and averaged [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: reports solution quality and latency as the scenario sample size 𝑁1 varies. For the C-SAA solver, total objective value decreases monotonically with 𝑁1, but average runtime grows roughly linearly to about 30 seconds at 𝑁1 = 90. The proxy, by contrast, attains its minimum objective at the training value 𝑁1 = 50 and degrades little for larger 𝑁1, with per-decision latency remaining near 0.006 seconds across … view at source ↗
read the original abstract

Sequential contextual stochastic programs model real-time decision systems in which each time epoch commits to an action under uncertainty whose consequences propagate into future decisions. In many practical contexts, these programs require obtaining solutions rapidly as new information becomes available. These problems can be represented through scenario approximations to be solved by off-the-shelf optimization solvers, which achieve high decision quality offline but typically run in seconds to minutes per instance, falling short of the sub-second responses that peak periods of planning require. This paper develops a learning-based optimization proxy: a scenario-embedded neural network trained offline on solver-generated labels, paired online with a decoder that enforces feasibility, replacing the per-epoch solve with a single forward pass. The framework is specialized to omnichannel order fulfillment, where each arriving order requires a sub-second assignment of products to distribution centers and carrier services under stochastic delivery times and future demand. A two-stage contextual stochastic program is introduced to formulate this problem, and its contextual sample average approximation (C-SAA) supplies the offline labels, while a composite training loss combines label imitation, a constraint-violation penalty, and self-supervised cost alignment. In a calibrated simulator built from JD.com transactional records, a detailed computational study is provided. The proxy reduces decision latency by roughly 2800x relative to the online finite-sample C-SAA reference and improves over it by 3.3% in realized fulfillment cost. Relative to established fulfillment policies, the proxy lowers total realized cost by at least 10.7% and roughly halves the late-delivery rate.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper introduces a learning-based optimization proxy for sequential contextual stochastic programs, consisting of a scenario-embedded neural network trained offline on labels from contextual sample average approximation (C-SAA) together with a feasibility-enforcing decoder. The approach is specialized to omnichannel order fulfillment, where each order must be assigned to distribution centers and carriers under stochastic delivery times and future demand. In a simulator calibrated to JD.com data, the proxy is reported to achieve roughly 2800x lower decision latency than online C-SAA while improving realized cost by 3.3% and outperforming established policies by at least 10.7% with halved late-delivery rates.

Significance. If the reported generalization holds, the work supplies a practical route to sub-second, high-quality decisions for sequential stochastic programs that are otherwise too slow for real-time use. The composite training loss (label imitation + constraint penalty + self-supervised cost alignment) and the explicit feasibility decoder are concrete technical contributions that could be reused in other contextual stochastic settings.

major comments (3)
  1. [computational study] Computational study section: the headline performance figures (2800x latency reduction, 3.3% cost improvement over C-SAA, 10.7% vs. baselines) are presented without stating the number of test instances, number of independent simulation runs, variance estimates, or any statistical significance tests. This omission makes it impossible to judge whether the reported margins are robust or sensitive to simulator calibration choices.
  2. [framework and computational study] Training and online deployment description: the central claim that the offline-trained network produces high-quality feasible decisions on unseen order sequences rests on an untested generalization assumption. No out-of-distribution experiments, temporal hold-out splits, or simulator-reality gap tests are described, so any mismatch between the training distribution of contexts and future sequences directly undermines the claimed online gains.
  3. [two-stage contextual stochastic program formulation] C-SAA label generation: the finite-sample C-SAA used to produce training labels is itself an approximation whose quality depends on the number of scenarios; the manuscript does not report how label quality varies with scenario count or how this propagates into proxy performance.
minor comments (2)
  1. [training loss] Notation for the composite loss function should be introduced with an explicit equation number rather than inline description.
  2. [computational study] The abstract states performance numbers to one decimal place; the computational study should include a table that reports the same metrics with standard deviations across runs.

Simulated Author's Rebuttal

3 responses · 0 unresolved

Thank you for the referee's constructive comments. We address each major point below and outline the revisions we will incorporate.

read point-by-point responses

  1. Referee: [computational study] Computational study section: the headline performance figures (2800x latency reduction, 3.3% cost improvement over C-SAA, 10.7% vs. baselines) are presented without stating the number of test instances, number of independent simulation runs, variance estimates, or any statistical significance tests. This omission makes it impossible to judge whether the reported margins are robust or sensitive to simulator calibration choices.

    Authors: We agree that the computational study would benefit from explicit reporting of these details. In the revision we will add the number of test instances, the number of independent simulation runs performed, variance or standard-error estimates, and any statistical significance tests conducted. revision: yes

  2. Referee: [framework and computational study] Training and online deployment description: the central claim that the offline-trained network produces high-quality feasible decisions on unseen order sequences rests on an untested generalization assumption. No out-of-distribution experiments, temporal hold-out splits, or simulator-reality gap tests are described, so any mismatch between the training distribution of contexts and future sequences directly undermines the claimed online gains.

    Authors: The reported results are obtained on order sequences generated inside the calibrated simulator that were not seen during training, which constitutes an in-distribution hold-out evaluation. We acknowledge that explicit out-of-distribution or temporal-split experiments and simulator-reality gap analysis are not currently described. We will revise the manuscript to clarify the existing train-test protocol and add a dedicated discussion of generalization limits. revision: partial

  3. Referee: [two-stage contextual stochastic program formulation] C-SAA label generation: the finite-sample C-SAA used to produce training labels is itself an approximation whose quality depends on the number of scenarios; the manuscript does not report how label quality varies with scenario count or how this propagates into proxy performance.

    Authors: We agree that sensitivity of label quality to the scenario count in C-SAA is an important missing analysis. The revised manuscript will include experiments that vary the number of scenarios used to generate labels and report the resulting effect on proxy performance. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical proxy training and simulator evaluation are independent of fitted inputs.

full rationale

The paper trains a neural network offline to imitate finite-sample C-SAA solutions generated by an external solver on a calibrated simulator, then evaluates the resulting proxy online inside the same simulator against the C-SAA reference and baseline policies. No equation or claim reduces a performance metric to a fitted parameter by construction, no self-citation is invoked as a uniqueness theorem, and the reported latency and cost improvements are measured quantities rather than redefinitions of the training loss. The derivation chain consists of standard supervised learning plus a feasibility decoder, with all quantitative claims resting on external simulation runs.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central performance claims rest on the representativeness of the JD.com-calibrated simulator and the quality of C-SAA labels for training a generalizable proxy.

free parameters (1)
  • neural network architecture and training hyperparameters
    Chosen to fit the offline C-SAA labels and simulator data.
axioms (2)
  • domain assumption C-SAA solver labels provide sufficiently high-quality training targets for the proxy.
    The proxy is trained to imitate these labels.
  • domain assumption The calibrated simulator accurately captures real-world stochastic dynamics and demand patterns.
    All reported results and comparisons are generated inside this simulator.

pith-pipeline@v0.9.1-grok · 5824 in / 1262 out tokens · 36065 ms · 2026-06-25T21:18:38.567402+00:00 · methodology

discussion (0)

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Reference graph

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