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

arXiv: https://arxiv.org/abs/2606.25362 · HTML: https://mlsanity.com/paper/2606.25362/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 39 references that are in the map.
- First posted on arXiv 24 Jun 2026.

## Builds on (most cited first, 20 of 20)

- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization](https://mlsanity.com/paper/1809.05504/) (2018)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [From Predictive to Prescriptive Analytics](https://mlsanity.com/paper/1402.5481/) (2014)
- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [End-to-End Feasible Optimization Proxies for Large-Scale Economic Dispatch](https://mlsanity.com/paper/2304.11726/) (2023)
- [Integrated Conditional Estimation-Optimization](https://mlsanity.com/paper/2110.12351/) (2021)
- [Neur2SP: Neural Two-Stage Stochastic Programming](https://mlsanity.com/paper/2205.12006/) (2022)
- [Optimization Learning](https://mlsanity.com/paper/2501.03443/) (2025)
- [Data-Driven Sample Average Approximation with Covariate Information](https://mlsanity.com/paper/2207.13554/) (2022)
- [Learning-based Online Optimization for Autonomous Mobility-on-Demand Fleet Control](https://mlsanity.com/paper/2302.03963/) (2023)
- [Scenario Predict-then-Optimize for Data-Driven Online Inventory Routing](https://mlsanity.com/paper/2401.17787/) (2024)
- [Control of Dual-Sourcing Inventory Systems using Recurrent Neural Networks](https://mlsanity.com/paper/2201.06126/) (2022)
- [Contextual Stochastic Optimization for Omnichannel Multi-Courier Order Fulfillment Under Delivery Time Uncertainty](https://mlsanity.com/paper/2409.06918/) (2024)
- [Machine Learning-Augmented Optimization of Large Bilevel and Two-stage Stochastic Programs: Application to Cycling Network Design](https://mlsanity.com/paper/2209.09404/) (2022)
- [Conformal Predictive Distributions for Order Fulfillment Time Forecasting](https://mlsanity.com/paper/2505.17340/) (2025)
- [Efficiently Training Deep-Learning Parametric Policies using Lagrangian Duality](https://mlsanity.com/paper/2405.14973/) (2024)
- [Uncertainty-Aware Delivery Delay Duration Prediction via Multi-Task Deep Learning](https://mlsanity.com/paper/2602.20271/) (2026)

## Abstract (arXiv)

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.