Distributional Robustness Regularized Scenario Optimization with Application to Model Predictive Control

TL;DR

This paper introduces a new approach to distributionally robust optimization using functional analysis, enabling effective model predictive control under distribution shifts with limited data.

Contribution

It presents two practical computational methods for distributionally robust nonlinear optimization based on gradient norms and reproducing kernel Hilbert spaces.

Findings

Effective constraint satisfaction with few scenarios under distribution shift

Applicable to small sample sizes in statistical learning

Robustifies scenario-based stochastic model predictive control

Abstract

We provide a functional view of distributional robustness motivated by robust statistics and functional analysis. This results in two practical computational approaches for approximate distributionally robust nonlinear optimization based on gradient norms and reproducing kernel Hilbert spaces. Our method can be applied to the settings of statistical learning with small sample size and test distribution shift. As a case study, we robustify scenario-based stochastic model predictive control with general nonlinear constraints. In particular, we demonstrate constraint satisfaction with only a small number of scenarios under distribution shift.