Riemannian Hamiltonian Methods for Min-Max Optimization on Manifolds
Riemannian Hamiltonian Methods for Min-Max Optimization on Manifolds
.In this paper, we study min-max optimization problems on Riemannian manifolds. We introduce a Riemannian Hamiltonian function, minimization of which serves as a proxy for solving the original min-max problems. Under the Riemannian Polyak–Łojasiewicz condition on the Hamiltonian function, its minimizer corresponds to the desired min-max saddle point. We also …