Breaking 1/epsilon Barrier in Quantum Zero-Sum Games: Generalizing Metric Subregularity for Spectraplexes
The research investigates whether quantum zero-sum games can achieve linear convergence rates to Nash equilibrium using gradient methods, similar to classical polyhedral cases. By proving metric subregularity for quantum feasible sets (spectraplexes), the paper shows that curved geometries do not prevent linear last-iterate convergence for algorithms like Nesterov’s smoothing and Optimistic Gradient Descent–Ascent (OGDA).