Data-Driven Moment-Based Distributionally Robust Chance-Constrained Optimization

TL;DR

This paper introduces a computationally efficient, data-driven approach to handle chance constraints in stochastic optimization by incorporating uncertainty in mean and covariance estimates, ensuring reliability without excessive conservatism.

Contribution

It proposes a novel modification of distributionally robust chance constraints that accounts for the randomness in sample mean and covariance, improving reliability in data-driven stochastic optimization.

Findings

Method is computationally fast and practical.

Achieves similar reliability to existing methods.

Less conservative than traditional approaches.

Abstract

Many stochastic optimization problems include chance constraints that enforce constraint satisfaction with a specific probability; however, solving an optimization problem with chance constraints assumes that the solver has access to the exact underlying probability distribution, which is often unreasonable. In data-driven applications, it is common instead to use historical data samples as a surrogate to the distribution; however, this comes at a significant computational cost from the added time spent either processing the data or, worse, adding additional variables and constraints to the optimization problem. On the other hand, the sample mean and covariance matrix are lightweight to calculate, and it is possible to reframe the chance constraint as a distributionally robust chance constraint. The challenge here is that the sample mean and covariance matrix themselves are random variables, so their uncertainty should be factored into the chance constraint. This work bridges this gap by modifying the standard method of distributionally robust chance constraints to guarantee its satisfaction. The proposed data-driven method is tested on a particularly problematic example. The results show that the computationally fast proposed method is not significantly more conservative than other methods.