ICNN-enhanced 2SP: Leveraging input convex neural networks for solving two-stage stochastic programming

TL;DR

The paper tackles the scalability bottleneck in two-stage stochastic programming by introducing ICNN-enhanced 2SP, which replaces MIP-based neural surrogates with Input Convex Neural Networks that admit exact LP-based inference. It provides a convexity-centered analysis across continuous and mixed-integer recourse cases, and demonstrates how to train and embed the ICNN surrogate within the 2SP framework to obtain a compact, LP-reformulated problem. Empirical results on CFLP, SSLP, and INVP show training efficiency comparable to standard neural surrogates and substantial solve-time speedups—up to 100x in some large-scale instances—without compromising solution quality. The work highlights the method’s practical relevance for time-sensitive decision problems while outlining convexity as a key limitation and potential avenues for extending to broader convex recourse settings.

Abstract

Two-stage stochastic programming (2SP) offers a basic framework for modelling decision-making under uncertainty, yet scalability remains a challenge due to the computational complexity of recourse function evaluation. Existing learning-based methods like Neural Two-Stage Stochastic Programming (Neur2SP) employ neural networks (NNs) as recourse function surrogates but rely on computationally intensive mixed-integer programming (MIP) formulations. We propose ICNN-enhanced 2SP, a method that leverages Input Convex Neural Networks (ICNNs) to exploit linear programming (LP) representability in convex 2SP problems. By architecturally enforcing convexity and enabling exact inference through LP, our approach eliminates the need for integer variables inherent to the conventional MIP-based formulation while retaining an exact embedding of the ICNN surrogate within the 2SP framework. This results in a more computationally efficient alternative, and we show that good solution quality can be maintained. Comprehensive experiments reveal that ICNNs incur only marginally longer training times while achieving validation accuracy on par with their standard NN counterparts. Across benchmark problems, ICNN-enhanced 2SP often exhibits considerably faster solution times than the MIP-based formulations while preserving solution quality, with these advantages becoming significantly more pronounced as problem scale increases. For the most challenging instances, the method achieves speedups of up to 100$\times$ and solution quality superior to MIP-based formulations.

Figures (2)

• Figure 1: Overview of the proposed optimisation methodology.
• Figure 2: Architecture of a fully connected ICNN.

Theorems & Definitions (1)

• Remark : Extension to nonlinear convex recourse