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Title: Variational Principles for Mirror Descent and Mirror Langevin Dynamics
Award ID(s):
2106358 1934986
PAR ID:
10413658
Author(s) / Creator(s):
 ;  ;  ;  
Publisher / Repository:
Institute of Electrical and Electronics Engineers
Date Published:
Journal Name:
IEEE Control Systems Letters
Volume:
7
ISSN:
2475-1456
Page Range / eLocation ID:
p. 1542-1547
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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    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.” 
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