Distributionally Robust Bootstrap Optimization

TL;DR

This paper introduces a new architecture combining bootstrap resampling with distributionally robust optimization to enhance robustness and provide safety guarantees in complex control systems.

Contribution

It presents a novel integration of bootstrap methods with distributionally robust optimization for layered control architectures.

Findings

Provides a finite-data out-of-sample safety guarantee.

Reformulates the approach as a tractable convex optimization problem.

Demonstrates improved robustness in control system design.

Abstract

Control architectures and autonomy stacks for complex engineering systems are often divided into layers to decompose a complex problem and solution into distinct, manageable sub-problems. To simplify designs, uncertainties are often ignored across layers, an approach with deep roots in classical notions of separation and certainty equivalence. But to develop robust architectures, especially as interactions between data-driven learning layers and model-based decision-making layers grow more intricate, more sophisticated interfaces between layers are required. We propose a basic architecture that couples a statistical parameter estimation layer with a constrained optimization layer. We show how the layers can be tightly integrated by combining bootstrap resampling with distributionally robust optimization. The approach allows a finite-data out-of-sample safety guarantee and an exact reformulation as a tractable finite-dimensional convex optimization problem.