# Learning-Based Surrogate Method for Stochastic Optimization under Decision-Dependent Uncertainty with Adaptive Random Designs

arXiv: https://arxiv.org/abs/2505.07298 · HTML: https://mlsanity.com/paper/2505.07298/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 41 references that are in the map.
- First posted on arXiv 12 May 2025.

## Builds on (most cited first, 14 of 14)

- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Stochastic model-based minimization of weakly convex functions](https://mlsanity.com/paper/1803.06523/) (2018)
- [Outside the Echo Chamber: Optimizing the Performative Risk](https://mlsanity.com/paper/2102.08570/) (2021)
- [Stochastic optimization with decision-dependent distributions](https://mlsanity.com/paper/2011.11173/) (2020)
- [Efficiency of minimizing compositions of convex functions and smooth maps](https://mlsanity.com/paper/1605.00125/) (2016)
- [Stochastic Methods for Composite and Weakly Convex Optimization Problems](https://mlsanity.com/paper/1703.08570/) (2017)
- [Proximally Guided Stochastic Subgradient Method for Nonsmooth, Nonconvex Problems](https://mlsanity.com/paper/1707.03505/) (2017)
- [Minibatch and Momentum Model-based Methods for Stochastic Weakly Convex Optimization](https://mlsanity.com/paper/2106.03034/) (2021)
- [Two-timescale Derivative Free Optimization for Performative Prediction with Markovian Data](https://mlsanity.com/paper/2310.05792/) (2023)
- [Nearest Neighbour Based Estimates of Gradients: Sharp Nonasymptotic Bounds and Applications](https://mlsanity.com/paper/2006.15043/) (2020)
- [Semi-Supervised Deep Sobolev Regression: Estimation and Variable Selection by ReQU Neural Network](https://mlsanity.com/paper/2401.04535/) (2024)
- [Distributionally Robust Facility Location Problem under Decision-dependent Stochastic Demand](https://mlsanity.com/paper/1912.05577/) (2019)
- [Zeroth-Order Methods for Nonconvex Stochastic Problems with Decision-Dependent Distributions](https://mlsanity.com/paper/2412.20330/) (2024)
- [Solving Two-Stage Stochastic Programs with Endogenous Uncertainty via Random Variable Transformation](https://mlsanity.com/paper/2402.15486/) (2024)

## Abstract (arXiv)

We study stochastic programs in which the latent decision-dependent uncertainty is described via a nonparametric regression model. The major challenge is that, without convexity assumptions on either the cost function or the regression model, the resulting objective is both nonconvex and nonsmooth, and its first-order information is unavailable due to the unknown decision-dependent distribution. To address this issue, we construct a learning-based surrogate model that integrates simulation and statistical learning by embedding Jacobian estimates of the regression function, which are updated iteratively and interactively during the optimization procedure. We develop an adaptive random design that concentrates design points around the current iterate for Jacobian estimation and we show that the mean squared error of Jacobian estimates achieves a dimension-independent convergence rate. Building on this, we propose the learning-based stochastic prox-linear (L-SPL) algorithm with adaptive random design and establish its nonasymptotic convergence rates under various parameter settings. Numerical results demonstrate that L-SPL algorithm significantly improves sample efficiency and achieves substantially lower objective values compared to the state-of-the-art methods. More broadly, our method implies that the statistical design in an iterative learning-based optimization algorithm can be novelly tailored to the local information of the optimization procedure to sharpen estimates and enhance the convergence performance and sample efficiency of the resulting algorithm.