Extend the analysis to the two-sided Polyak–Łojasiewicz setting

Extend the lower-bound construction and oracle-complexity analysis to two-sided Polyak–Łojasiewicz minimax optimization, in which both the primal and dual variables satisfy a Polyak–Łojasiewicz condition, in order to characterize the resulting complexity landscape.

Background

The results concern the NC-P class, where the objective satisfies a Polyak–Łojasiewicz condition only in the dual variable, while the value function is nonconvex in the primal variable. The paper explicitly distinguishes this setting from the two-sided P setting, in which the primal variable also satisfies a P condition.

Because the existing construction does not cover the two-sided P setting and the authors note that it has a different upper-bound landscape, extending the lower-bound framework or otherwise characterizing oracle complexity there remains unresolved.