We present a primal only derivation of Mirror Descent as a "partial" discretization of gradient flow on a Riemannian manifold where the metric tensor is the Hessian of the Mirror Descent potential. We contrast this discretization to Natural Gradient Descent, which is obtained by a "full" forward Euler discretization. This view helps shed light on the relationship between the methods and allows generalizing Mirror Descent to general Riemannian geometries, even when the metric tensor is {\em not} a Hessian, and thus there is no "dual."

翻译：我们将“ 镜光源” 的原始衍生物作为“ 部分” 分解的梯度流在里曼尼方形中, 其度高是“ 镜光源潜力的赫西安 ” 。 我们将这种分解与“ 完全” 远端“ 分解” 获得的自然梯度源进行对比。 这个观点有助于揭示方法之间的关系, 并允许将镜光源向一般的里曼尼地貌分布开来, 即使光度分母不是赫西安人, 因此没有“ 双向” 。