论文标题
无反光镜下降：镜下降的自然推导
Mirrorless Mirror Descent: A Natural Derivation of Mirror Descent
论文作者
论文摘要
我们提出了镜下降的原始推导，作为在riemannian歧管上梯度流的“部分”离散化，其中度量张量是镜下降电位的Hessian。我们将这种离散化与自然梯度下降进行了对比，该梯度下降是通过“完整”前进Euler离散化获得的。这种观点有助于阐明方法之间的关系，并允许将镜像概括为一般的riemannian几何形状，即使度量张量为{\ em not}是Hessian，因此没有“ dual”。
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."
