161 research outputs found
Data-driven Piecewise Affine Decision Rules for Stochastic Programming with Covariate Information
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
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