Distributionally Robust Regret Optimal Control Under Moment-Based Ambiguity Sets

TL;DR

This paper develops a distributionally robust control method for linear-quadratic problems with moment-based ambiguity sets, providing a convex reformulation and scalable algorithms for worst-case regret minimization.

Contribution

It introduces a novel robust control approach using moment-based ambiguity sets, with a convex reformulation and a scalable subgradient method for optimal control.

Findings

The convex reformulation enables efficient computation of robust controllers.

The proposed method outperforms existing data-driven control techniques in experiments.

Abstract

We consider a class of finite-horizon, linear-quadratic stochastic control problems, where the probability distribution governing the noise process is unknown but assumed to belong to an ambiguity set consisting of all distributions whose mean and covariance lie within norm balls centered at given nominal values. To cope with this ambiguity, we design causal affine control policies to minimize the worst-case expected regret over all distributions in the ambiguity set. The resulting minimax optimal control problem is shown to admit an equivalent reformulation as a tractable convex program, which can be interpreted as a regularized version of the nominal linear-quadratic stochastic control problem. Based on the dual of this convex reformulation, we develop a scalable projected subgradient method for computing optimal controllers to arbitrary accuracy. Numerical experiments are provided to compare the proposed method with state-of-the-art data-driven control design methods.