Adaptive Learning-based Surrogate Method for Stochastic Programs with Implicitly Decision-dependent Uncertainty

TL;DR

This paper introduces an adaptive learning-based surrogate method for complex stochastic programming problems with decision-dependent uncertainty, improving computational stability and convergence through integrated simulation and statistical estimation.

Contribution

The paper develops a novel adaptive surrogate approach that combines simulation and statistical estimates to handle decision-dependent uncertainty in stochastic programs, with proven convergence guarantees.

Findings

Demonstrates superior convergence rates and stability in theory.

Shows improved efficiency and robustness in numerical experiments.

Validates effectiveness on synthetic and real datasets.

Abstract

We consider a class of stochastic programming problems where the implicitly decision-dependent random variable follows a nonparametric regression model with heteroscedastic error. The Clarke subdifferential and surrogate functions are not readily obtainable due to the latent decision dependency. To deal with such a computational difficulty, we develop an adaptive learning-based surrogate method that integrates the simulation scheme and statistical estimates to construct estimation-based surrogate functions in a way that the simulation process is adaptively guided by the algorithmic procedure. We establish the non-asymptotic convergence rate analysis in terms of $(\nu, \delta)$-near stationarity in expectation under variable proximal parameters and batch sizes, which exhibits the superior convergence performance and enhanced stability in both theory and practice. We provide numerical results with both synthetic and real data which illustrate the benefits of the proposed algorithm in terms of algorithmic stability and efficiency.