Distributionally Robust Control with Constraints on Linear Unidimensional Projections

TL;DR

This paper introduces iterative methods for distributionally robust control problems constrained by linear projection expectations, enabling approximate solutions in complex scenarios like portfolio and trajectory planning.

Contribution

It proposes two novel iterative algorithms for solving a broad class of distributionally robust control problems with linear projection constraints.

Findings

Algorithms effectively solve robust control problems with linear projection constraints.

Methods are applicable to portfolio construction and trajectory planning.

Proposed approaches provide approximate solutions in complex, real-world scenarios.

Abstract

Distributionally robust control is a well-studied framework for optimal decision making under uncertainty, with the objective of minimizing an expected cost function over control actions, assuming the most adverse probability distribution from an ambiguity set. We consider an interpretable and expressive class of ambiguity sets defined by constraints on the expected value of functions of one-dimensional linear projections of the uncertain parameters. Prior work has shown that, under conditions, problems in this class can be reformulated as finite convex problems. In this work, we propose two iterative methods that can be used to approximately solve problems of this class in the general case. The first is an approximate algorithm based on best-response dynamics. The second is an approximate method that first reformulates the problem as a semi-infinite program and then solves a relaxation. We apply our methods to portfolio construction and trajectory planning scenarios.