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A Symplectic Analysis of Alternating Mirror Descent
May 7, 2024, 4:44 a.m. | Jonas Katona, Xiuyuan Wang, Andre Wibisono
cs.LG updates on arXiv.org arxiv.org
Abstract: Motivated by understanding the behavior of the Alternating Mirror Descent (AMD) algorithm for bilinear zero-sum games, we study the discretization of continuous-time Hamiltonian flow via the symplectic Euler method. We provide a framework for analysis using results from Hamiltonian dynamics, Lie algebra, and symplectic numerical integrators, with an emphasis on the existence and properties of a conserved quantity, the modified Hamiltonian (MH), for the symplectic Euler method. We compute the MH in closed-form when the …
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