# Data-driven Piecewise Affine Decision Rules for Stochastic Programming with Covariate Information

arXiv: https://arxiv.org/abs/2304.13646 · HTML: https://mlsanity.com/paper/2304.13646/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 44 references that are in the map.
- First posted on arXiv 26 Apr 2023.

## Builds on (most cited first, 7 of 7)

- [From Predictive to Prescriptive Analytics](https://mlsanity.com/paper/1402.5481/) (2014)
- [Stochastic Optimization for DC Functions and Non-smooth Non-convex Regularizers with Non-asymptotic Convergence](https://mlsanity.com/paper/1811.11829/) (2018)
- [Piecewise Linear Regression via a Difference of Convex Functions](https://mlsanity.com/paper/2007.02422/) (2020)
- [Data-Driven Sample Average Approximation with Covariate Information](https://mlsanity.com/paper/2207.13554/) (2022)
- [Composite Difference-Max Programs for Modern Statistical Estimation Problems](https://mlsanity.com/paper/1803.00205/) (2018)
- [Minibatch and Momentum Model-based Methods for Stochastic Weakly Convex Optimization](https://mlsanity.com/paper/2106.03034/) (2021)
- [On the Finite Number of Directional Stationary Values of Piecewise Programs](https://mlsanity.com/paper/1803.00190/) (2018)

## Built on by (most cited first, 4 of 4)

- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [Escaping Local Minima Provably in Non-convex Matrix Sensing: A Deterministic Framework via Simulated Lifting](https://mlsanity.com/paper/2602.05887/) (2026)
- [Smart Surrogate Losses for Contextual Stochastic Linear Optimization with Robust Constraints](https://mlsanity.com/paper/2505.22881/) (2025)
- [Smooth Learning with Hard Constraints via Legendre-Regularized Policies](https://mlsanity.com/paper/2607.24007/) (2026)

## Abstract (arXiv)

Focusing on stochastic programming (SP) with covariate information, this paper proposes an empirical risk minimization (ERM) method embedded within a nonconvex piecewise affine decision rule (PADR), which aims to learn the direct mapping from features to optimal decisions. We establish the nonasymptotic consistency result of our PADR-based ERM model for unconstrained problems and asymptotic consistency result for constrained ones. To solve the nonconvex and nondifferentiable ERM problem, we develop an enhanced stochastic majorization-minimization algorithm and establish the asymptotic convergence to (composite strong) directional stationarity along with complexity analysis. We show that the proposed PADR-based ERM method applies to a broad class of nonconvex SP problems with theoretical consistency guarantees and computational tractability. Our numerical study demonstrates the superior performance of PADR-based ERM methods compared to state-of-the-art approaches under various settings, with significantly lower costs, less computation time, and robustness to feature dimensions and nonlinearity of the underlying dependency.