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Title: Mirrorless Mirror Descent: A Natural Derivation of Mirror Descent
We present a direct (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 function. 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 any Riemannian geometry in Rd, even when the metric tensor is not a Hessian, and thus there is no “dual.”  more » « less
Award ID(s):
1764032
NSF-PAR ID:
10287063
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Proceedings of Machine Learning Research
Volume:
130
ISSN:
2640-3498
Page Range / eLocation ID:
2305-2313
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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