Higher-order methods for convex-concave min-max optimization and monotone variational inequalities

9 Jul 2020Brian BullinsKevin A. Lai

We provide improved convergence rates for constrained convex-concave min-max problems and monotone variational inequalities with higher-order smoothness. In min-max settings where the $p^{th}$-order derivatives are Lipschitz continuous, we give an algorithm HigherOrderMirrorProx that achieves an iteration complexity of $O(1/T^{\frac{p+1}{2}})$ when given access to an oracle for finding a fixed point of a $p^{th}$-order equation... (read more)

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