We examine the continuous-time counterpart of mirror descent, namely mirror
flow, on classification problems which are linearly separable. Such problems
are minimised `at infinity' and have many possible solutions; we study which
solution is preferred by the algorithm depending on the mirror potential. For
exponential tailed losses and under mild assumptions on the potential, we show
that the iterates converge in direction towards a $\phi_\infty$-maximum margin
classifier. The function $\phi_\infty$ is the $\textit{horizon function}$ of
the mirror potential and characterises its shape `at infinity'. When the
potential is separable, a simple formula allows to compute this function. We
analyse several examples of potentials and provide numerical experiments
highlighting our results.

我们研究了线性可分的分类问题上，镜像流作为镜像下降的连续时间对应物。对于指数尾部损失函数和对镜像势能的适度假设，在镜像势能的限制函数方向上，我们证明了迭代会收敛到一个最大间隔分类器的 phi 无穷值。当势能是可分离的时候，一个简单的公式能够计算这个函数。我们分析了几个势能的示例，并提供了强调我们结果的数值实验。