# On Data-Driven Prescriptive Analytics with Side Information: A Regularized Nadaraya-Watson Approach

arXiv: https://arxiv.org/abs/2110.04855 · HTML: https://mlsanity.com/paper/2110.04855/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Oct 2021.

## Built on by (most cited first, 12 of 12)

- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [Integrated Conditional Estimation-Optimization](https://mlsanity.com/paper/2110.12351/) (2021)
- [Estimate-Then-Optimize versus Integrated-Estimation-Optimization versus Sample Average Approximation: A Stochastic Dominance Perspective](https://mlsanity.com/paper/2304.06833/) (2023)
- [Optimizer's Information Criterion: Dissecting and Correcting Bias in Data-Driven Optimization](https://mlsanity.com/paper/2306.10081/) (2023)
- [Contextual Optimization under Covariate Shift: A Robust Approach by Intersecting Wasserstein Balls](https://mlsanity.com/paper/2406.02426/) (2024)
- [PolyFootNet: Extracting Polygonal Building Footprints in Off-Nadir Remote Sensing Images](https://mlsanity.com/paper/2408.08645/) (2024)
- [Robust Data-driven Prescriptiveness Optimization](https://mlsanity.com/paper/2306.05937/) (2023)
- ["Over-optimizing" for Normality: Budget-constrained Uncertainty Quantification for Contextual Decision-making](https://mlsanity.com/paper/2503.12747/) (2025)
- [Contextual Preference Distribution Learning](https://mlsanity.com/paper/2603.17139/) (2026)
- [Deployment of AI-Assisted Interventions: Capacity Constraints and Noisy Compliance](https://mlsanity.com/paper/2604.14370/) (2026)
- [Smooth Learning with Hard Constraints via Legendre-Regularized Policies](https://mlsanity.com/paper/2607.24007/) (2026)
- [Decision-Driven Regularization: A Blended Model for Learning and Optimization](https://mlsanity.com/paper/2608.15124/) (2026)

## Abstract (arXiv)

We consider generic stochastic optimization problems in the presence of side information which enables a more insightful decision. The side information constitutes observable exogenous covariates that alter the conditional probability distribution of the random problem parameters. A decision maker who adapts her decisions according to the observed side information solves an optimization problem where the objective function is specified by the conditional expectation of the random cost. If the joint probability distribution is unknown, then the conditional expectation can be approximated in a data-driven manner using the Nadaraya-Watson (NW) kernel regression. While the emerging approximation scheme has found successful applications in diverse decision problems under uncertainty, it is largely unknown whether the scheme can provide any reasonable out-of-sample performance guarantees. In this paper, we establish guarantees for the generic problems by leveraging techniques from moderate deviations theory. Our analysis motivates the use of a variance-based regularization scheme which, in general, leads to a non-convex optimization problem. We adopt ideas from distributionally robust optimization to obtain tractable formulations. We present numerical experiments for newsvendor and wind energy commitment problems to highlight the effectiveness of our regularization scheme.