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

• 成果类型: Article; Early Access
• 署名作者: Zhang, Yiyang; Liu, Junyi; Zhaoa, Xiaobo
• 署名单位: Tsinghua University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2023.0175
• 发表日期: 2026
• 关键词: Approximation; algorithms

摘要

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 PADRbased ERM model for unconstrained problems, which illustrates the role of piece number in balancing the trade-off between the approximation and estimation errors. To solve the non-convex and nondifferentiable ERM problem, we develop an enhanced stochastic majorization-minimization algorithm and establish the convergence to (composite strong) directional stationarity, along with convergence rate 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. Numerical experiments show that PADR significantly lowers costs with less computation time, and is more robust to feature dimensions and nonlinearity of the underlying dependency.