Data-Driven Approximations of Chance Constrained Programs in Nonstationary Environments

TL;DR

This paper introduces a robust sample average approximation method for chance constrained programs in nonstationary environments, accounting for changing data distributions using Wasserstein distance, and provides distribution-free sample size estimates.

Contribution

It proposes a novel robust SAA approach that handles nonstationary data and offers distribution-free guarantees for solution feasibility.

Findings

Provides distribution-free sample size bounds for nonstationary data

Develops a Wasserstein-based robust SAA method

Ensures high-confidence feasibility under changing distributions

Abstract

We study sample average approximations (SAA) of chance constrained programs. SAA methods typically approximate the actual distribution in the chance constraint using an empirical distribution constructed from random samples assumed to be independent and identically distributed according to the actual distribution. In this paper, we consider a nonstationary variant of this problem, where the random samples are assumed to be independently drawn in a sequential fashion from an unknown and possibly time-varying distribution. This nonstationarity may be driven by changing environmental conditions present in many real-world applications. To account for the potential nonstationarity in the data generation process, we propose a novel robust SAA method exploiting information about the Wasserstein distance between the sequence of data-generating distributions and the actual chance constraint distribution. As a key result, we obtain distribution-free estimates of the sample size required to ensure that the robust SAA method will yield solutions that are feasible for the chance constraint under the actual distribution with high confidence.