# Predict-then-Calibrate: A New Perspective of Robust Contextual LP

arXiv: https://arxiv.org/abs/2305.15686 · HTML: https://mlsanity.com/paper/2305.15686/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 May 2023.

## Built on by (most cited first, 17 of 17)

- [Conformal Contextual Robust Optimization](https://mlsanity.com/paper/2310.10003/) (2023)
- [End-to-end Conditional Robust Optimization](https://mlsanity.com/paper/2403.04670/) (2024)
- [End-to-End Conformal Calibration for Optimization Under Uncertainty](https://mlsanity.com/paper/2409.20534/) (2024)
- [Conformal Prediction for Ensembles: Improving Efficiency via Score-Based Aggregation](https://mlsanity.com/paper/2405.16246/) (2024)
- [Differentiable Distributionally Robust Optimization Layers](https://mlsanity.com/paper/2406.16571/) (2024)
- [Conformalized Interval Arithmetic with Symmetric Calibration](https://mlsanity.com/paper/2408.10939/) (2024)
- [Robust Losses for Decision-Focused Learning](https://mlsanity.com/paper/2310.04328/) (2023)
- [Enhanced Route Planning with Calibrated Uncertainty Set](https://mlsanity.com/paper/2503.10088/) (2025)
- [A Conformal Approach to Feature-based Newsvendor under Model Misspecification](https://mlsanity.com/paper/2412.13159/) (2024)
- [Smart Surrogate Losses for Contextual Stochastic Linear Optimization with Robust Constraints](https://mlsanity.com/paper/2505.22881/) (2025)
- [Non-collective Calibrating Strategy for Time Series Forecasting](https://mlsanity.com/paper/2506.03176/) (2025)
- [Epistemic Robust Offline Reinforcement Learning](https://mlsanity.com/paper/2604.07072/) (2026)
- [From Data to Uncertainty Sets: a Machine Learning Approach](https://mlsanity.com/paper/2503.02173/) (2025)
- [Contextual Preference Distribution Learning](https://mlsanity.com/paper/2603.17139/) (2026)
- [Decision-Calibrated Conformal Uncertainty for Pacing Decisions in Streaming Advertising](https://mlsanity.com/paper/2606.10187/) (2026)
- [Learning Predictive Ambiguity Sets for Decision-Focused Distributionally Robust Optimization](https://mlsanity.com/paper/2607.09820/) (2026)
- [Smart predict-then-robustly-optimize](https://mlsanity.com/paper/2607.21773/) (2026)

## Abstract (arXiv)

Contextual optimization, also known as predict-then-optimize or prescriptive analytics, considers an optimization problem with the presence of covariates (context or side information). The goal is to learn a prediction model (from the training data) that predicts the objective function from the covariates, and then in the test phase, solve the optimization problem with the covariates but without the observation of the objective function. In this paper, we consider a risk-sensitive version of the problem and propose a generic algorithm design paradigm called predict-then-calibrate. The idea is to first develop a prediction model without concern for the downstream risk profile or robustness guarantee, and then utilize calibration (or recalibration) methods to quantify the uncertainty of the prediction. While the existing methods suffer from either a restricted choice of the prediction model or strong assumptions on the underlying data, we show the disentangling of the prediction model and the calibration/uncertainty quantification has several advantages. First, it imposes no restriction on the prediction model and thus fully unleashes the potential of off-the-shelf machine learning methods. Second, the derivation of the risk and robustness guarantee can be made independent of the choice of the prediction model through a data-splitting idea. Third, our paradigm of predict-then-calibrate applies to both (risk-sensitive) robust and (risk-neutral) distributionally robust optimization (DRO) formulations. Theoretically, it gives new generalization bounds for the contextual LP problem and sheds light on the existing results of DRO for contextual LP. Numerical experiments further reinforce the advantage of the predict-then-calibrate paradigm in that an improvement on either the prediction model or the calibration model will lead to a better final performance.