Optimality of Linear Policies in Distributionally Robust Linear Quadratic Control

How much distributional ambiguity can classical LQG control absorb? Across a broad family of divergence-based uncertainty sets, we prove that the worst-case noise distribution remains Gaussian and that a policy linear in the observations remains optimal. The adversary responds to uncertainty by inflating the noise covariance rather than shifting its mean. These structural results preserve the familiar form of LQG control even when the noise distribution is not known precisely.

Advances in Neural Information Processing Systems (NeurIPS)