Gradient dominance (benign property) of the IOH‑parameterized LQG cost

Determine whether the IOH‑parameterized LQG cost function J(K) over the set of stabilizing IOH gains K satisfies gradient‑dominance (Polyak–Łojasiewicz) or similar benign optimization properties that would enable strong global convergence guarantees for gradient‑based methods.

Background

In IOH parameterization, dynamic output‑feedback controller design is recast as static partial‑state feedback on a measurable IOH state, yielding a structured state‑feedback policy. While LQR state‑feedback problems enjoy benign properties such as gradient dominance that enable global convergence of PGMs, the IOH‑based LQG cost remains difficult to analyze.

The paper shows convergence to O(ε)‑stationary points via a relaxed coercive cost but does not establish whether the original cost J(K) possesses gradient‑dominance or related benign properties; resolving this would strengthen theoretical guarantees for PGMs in IOH‑based LQG control.