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

2025-05-12

AI Summary

This paper addresses decision-dependent stochastic programming, where uncertainty is modeled via heteroscedastic nonparametric regression—rendering Clarke subgradients and classical surrogate functions analytically intractable. To overcome this, we propose an adaptive learning-based surrogate optimization framework: it jointly leverages Monte Carlo simulation and dynamic nonparametric estimation to construct surrogates; and introduces a (( u,delta))-approximate stationarity analysis with variable proximal parameters and adaptive batch sizes, yielding non-asymptotic convergence guarantees. Theoretically, our method achieves faster convergence rates and significantly improved stability compared to existing approaches. Empirical evaluations on synthetic and real-world datasets demonstrate substantial gains in both robustness and computational efficiency. The core contribution lies in the first integration of adaptive statistical learning into decision-dependent stochastic optimization—thereby circumventing the long-standing limitation of unavailable subgradients in such settings.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Economics, Online Markets and Human Computation: Social networks and social learning
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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 $( u, delta)$-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.

Problem

• Handles stochastic programs with decision-dependent uncertainty
• Develops adaptive learning-based surrogate method
• Ensures convergence and stability in nonparametric regression

Innovation

• Adaptive learning-based surrogate method
• Simulation-guided statistical estimates
• Non-asymptotic convergence rate analysis