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arXiv · 2004.01025

Mirrorless Mirror Descent: A Natural Derivation of Mirror Descent

Suriya Gunasekar·Blake Woodworth·Nathan Srebro
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Abstract

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."

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Suriya Gunasekar, Blake Woodworth, Nathan Srebro. 2020-04-02. Mirrorless Mirror Descent: A Natural Derivation of Mirror Descent. https://arxiv.org/abs/2004.01025

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