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

TL;DR

This paper introduces ICNN-enhanced 2SP, a novel approach that uses input convex neural networks to improve the scalability and efficiency of solving two-stage stochastic programming problems by leveraging LP representability.

Contribution

It proposes a new method combining ICNNs with 2SP to eliminate MIP complexity, enabling faster solutions while maintaining accuracy and solution quality.

Findings

Achieves up to 100x speedup on challenging instances.

Maintains comparable validation accuracy to standard neural networks.

Significantly faster solution times as problem scale increases.

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.