# A bilevel framework for decision-making under uncertainty with contextual information

arXiv: https://arxiv.org/abs/2008.01500 · HTML: https://mlsanity.com/paper/2008.01500/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Aug 2020.

## Built on by (most cited first, 13 of 13)

- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
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- [Prescribing net demand for two-stage electricity generation scheduling](https://mlsanity.com/paper/2108.01003/) (2021)
- [Application-Driven Learning: A Closed-Loop Prediction and Optimization Approach Applied to Dynamic Reserves and Demand Forecasting](https://mlsanity.com/paper/2102.13273/) (2021)
- [Towards Improving Unit Commitment Economics: An Add-On Tailor for Renewable Energy and Reserve Predictions](https://mlsanity.com/paper/2208.13065/) (2022)
- [Forecasting Outside the Box: Application-Driven Optimal Pointwise Forecasts for Stochastic Optimization](https://mlsanity.com/paper/2411.03520/) (2024)
- [Decision-focused predictions via pessimistic bilevel optimization: complexity and algorithms](https://mlsanity.com/paper/2312.17640/) (2023)
- [Evaluation of Prosumer Networks for Peak Load Management in Iran: A Distributed Contextual Stochastic Optimization Approach](https://mlsanity.com/paper/2409.00493/) (2024)
- [Learning-Augmented Power System Operations: A Unified Optimization View](https://mlsanity.com/paper/2505.05203/) (2025)
- [Decision-Focused Continual Learning for Seaport Power-Logistics Scheduling: Generalization across Varying Tasks](https://mlsanity.com/paper/2511.07938/) (2025)
- [Decision-Driven Regularization: A Blended Model for Learning and Optimization](https://mlsanity.com/paper/2608.15124/) (2026)

## Abstract (arXiv)

In this paper, we propose a novel approach for data-driven decision-making under uncertainty in the presence of contextual information. Given a finite collection of observations of the uncertain parameters and potential explanatory variables (i.e., the contextual information), our approach fits a parametric model to those data that is specifically tailored to maximizing the decision value, while accounting for possible feasibility constraints. From a mathematical point of view, our framework translates into a bilevel program, for which we provide both a fast regularization procedure and a big-M-based reformulation that can be solved using off-the-shelf optimization solvers. We showcase the benefits of moving from the traditional scheme for model estimation (based on statistical quality metrics) to decision-guided prediction using three different practical problems. We also compare our approach with existing ones in a realistic case study that considers a strategic power producer that participates in the Iberian electricity market. Finally, we use these numerical simulations to analyze the conditions (in terms of the firm's cost structure and production capacity) under which our approach proves to be more advantageous to the producer.