Neur2SP: Neural Two-Stage Stochastic Programming
This provides a faster, structure-agnostic solution method for decision-making under uncertainty in operations research, though it is incremental as it builds on existing neural network approximations for optimization.
The paper tackles the computational intractability of solving two-stage stochastic programs (2SPs), especially with mixed-integer or nonlinear second-stage problems, by developing Neur2SP, a method that approximates the expected value function with a neural network to enable efficient solving. It demonstrates that Neur2SP finds high-quality solutions in under 1.66 seconds across various benchmarks, outperforming traditional methods that take minutes to hours.
Stochastic Programming is a powerful modeling framework for decision-making under uncertainty. In this work, we tackle two-stage stochastic programs (2SPs), the most widely used class of stochastic programming models. Solving 2SPs exactly requires optimizing over an expected value function that is computationally intractable. Having a mixed-integer linear program (MIP) or a nonlinear program (NLP) in the second stage further aggravates the intractability, even when specialized algorithms that exploit problem structure are employed. Finding high-quality (first-stage) solutions -- without leveraging problem structure -- can be crucial in such settings. We develop Neur2SP, a new method that approximates the expected value function via a neural network to obtain a surrogate model that can be solved more efficiently than the traditional extensive formulation approach. Neur2SP makes no assumptions about the problem structure, in particular about the second-stage problem, and can be implemented using an off-the-shelf MIP solver. Our extensive computational experiments on four benchmark 2SP problem classes with different structures (containing MIP and NLP second-stage problems) demonstrate the efficiency (time) and efficacy (solution quality) of Neur2SP. In under 1.66 seconds, Neur2SP finds high-quality solutions across all problems even as the number of scenarios increases, an ideal property that is difficult to have for traditional 2SP solution techniques. Namely, the most generic baseline method typically requires minutes to hours to find solutions of comparable quality.