Abstract
We study the alternating mirror descent algorithm for a two-player constrained bilinear zero-sum game. We highlight the connection between alternating mirror descent as a symplectic discretization of a Hamiltonian flow in the dual space. We show a regret bound for alternating mirror descent under decreasing step size. We also study when we can show a regret bound with constant step size, similar to the unconstrained case (alternating gradient descent).