Applicability of Inexact Proximal-Point Extensions to State-Feedback H-Infinity Policy Optimization

Determine whether the extensions of the inexact proximal-point framework for hidden convex optimization developed by Fatkhullin et al. are directly applicable to state-feedback \(\mathcal{H}_\infty\) policy optimization.

Background

The paper compares its convex-lifting formulation with prior inexact proximal-point methods for hidden convex problems. Those methods primarily treat hidden convexity induced by a direct bijective transformation of the decision variable and typically assume convex, closed domains. In contrast, state-feedback H∞\mathcal{H}_\infty policy optimization involves additional Lyapunov lifting variables and an open, potentially nonconvex stabilizing-policy domain. The authors therefore identify the direct applicability of the prior extensions to this control problem as unresolved.

References

Although also studied functionally constrained problems, and discussed generalizations where the invertibility of $c$ can be relaxed, it is not yet clear whether such extensions are directly applicable to the state-feedback $\mathcal{H}_\infty$ policy optimization problem.

— Zeroth-Order Nonsmooth Nonconvex Optimization with Convex Liftings and Its Application to State-Feedback $H_\infty$ Policy Optimization  (2608.23178 - Wang et al., 24 Aug 2026) in Section 3.1, comparison with Fatkhullin et al.