STay-ON-the-Ridge: Guaranteed Convergence to Local Minimax Equilibrium in Nonconvex-Nonconcave Games. (arXiv:2210.09769v1 [cs.LG])

Min-max optimization problems involving nonconvex-nonconcave objectives have
found important applications in adversarial training and other multi-agent
learning settings. Yet, no known gradient descent-based method is guaranteed to
converge to (even local notions of) min-max equilibrium in the
nonconvex-nonconcave setting. For all known methods, there exist relatively
simple objectives for which they cycle or exhibit other undesirable behavior
different from converging to a point, let alone to some game-theoretically
meaningful one~\cite{flokas2019poincare,hsieh2021limits}. The only known
convergence guarantees hold under the strong assumption …

arxiv convergence equilibrium games minimax ridge