# A Deep Generative Learning Approach for Two-stage Adaptive Robust Optimization

arXiv: https://arxiv.org/abs/2409.03731 · HTML: https://mlsanity.com/paper/2409.03731/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 40 references that are in the map.
- First posted on arXiv 5 Sep 2024.

## Builds on (most cited first, 17 of 17)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Reliable Fidelity and Diversity Metrics for Generative Models](https://mlsanity.com/paper/2002.09797/) (2020)
- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [Cyclical Annealing Schedule: A Simple Approach to Mitigating KL Vanishing](https://mlsanity.com/paper/1903.10145/) (2019)
- [Interactive Supercomputing on 40,000 Cores for Machine Learning and Data Analysis](https://mlsanity.com/paper/1807.07814/) (2018)
- [Robust Optimization using Machine Learning for Uncertainty Sets](https://mlsanity.com/paper/1407.1097/) (2014)
- [Learning-based Robust Optimization: Procedures and Statistical Guarantees](https://mlsanity.com/paper/1704.04342/) (2017)
- [Electric-Gas Infrastructure Planning for Deep Decarbonization of Energy Systems](https://mlsanity.com/paper/2212.13655/) (2022)
- [A Machine Learning Approach to Two-Stage Adaptive Robust Optimization](https://mlsanity.com/paper/2307.12409/) (2023)
- [Combating Conservativeness in Data-Driven Optimization under Uncertainty: A Solution Path Approach](https://mlsanity.com/paper/1909.06477/) (2019)
- [On the Solution of Large-Scale Robust Transmission Network Expansion Planning under Uncertain Demand and Generation Capacity](https://mlsanity.com/paper/1609.07902/) (2016)
- [A computationally efficient Benders decomposition for energy systems planning problems with detailed operations and time-coupling constraints](https://mlsanity.com/paper/2302.10037/) (2023)

## Built on by (most cited first, 2 of 2)

- [Learning Scenario Reduction for Two-Stage Robust Optimization with Discrete Uncertainty](https://mlsanity.com/paper/2605.14494/) (2026)
- [Generative Robust Optimisation](https://mlsanity.com/paper/2606.22536/) (2026)

## Abstract (arXiv)

Two-stage adaptive robust optimization (ARO) is a powerful approach for planning under uncertainty, balancing first-stage decisions with recourse decisions made after uncertainty is realized. To account for uncertainty, modelers typically define a simple uncertainty set over which potential outcomes are considered. However, classical methods for defining these sets unintentionally capture a wide range of unrealistic outcomes, resulting in overly-conservative and costly planning in anticipation of unlikely contingencies. In this work, we introduce AGRO, a solution algorithm that performs adversarial generation for two-stage adaptive robust optimization using a variational autoencoder. AGRO generates high-dimensional contingencies that are simultaneously adversarial and realistic, improving the robustness of first-stage decisions at a lower planning cost than standard methods. To ensure generated contingencies lie in high-density regions of the uncertainty distribution, AGRO defines a tight uncertainty set as the image of "latent" uncertainty sets under the VAE decoding transformation. Projected gradient ascent is then used to maximize recourse costs over the latent uncertainty sets by leveraging differentiable optimization methods. We demonstrate the cost-efficiency of AGRO by applying it to both a synthetic production-distribution problem and a real-world power system expansion setting. We show that AGRO outperforms the standard column-and-constraint algorithm by up to 1.8% in production-distribution planning and up to 11.6% in power system expansion.