Mirror Descent
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Group Entropies and Mirror Duality: A Class of Flexible Mirror Descent Updates for Machine Learning
arXiv:2603.08651v2 Announce Type: replace Abstract: We introduce a comprehensive theoretical and algorithmic framework that bridges formal group theory and group entropies with modern machine learning, paving the way for an infinite, flexible family of Mirror Descent (MD) optimization algorithms. Our approach exploits the rich structure of group entropies, which are generalized entropic functionals governed by group composition laws, encompassing and significantly extending all trace-form...
A Unified Variational Design of Predictive Mirror Descent in Convex Games under Stochastic Feedback
Announce Type: cross Abstract: Mirror descent provides a geometric framework for learning in games, but its last-iterate behavior can fail in weakly stable regimes, where the dynamics may exhibit rotational or recurrent transients. Predictive mirror methods mitigate this issue by modifying the feedback entering the mirror update, yet standard predictive variants are typically introduced algorithmically and analyzed one at a time. This letter gives a variational route to predictive feedback...
Bregman meets L\'evy: Stochastic mirror descent with heavy-tailed noise in continuous and discrete time
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Mirror Descent Under Generalized Smoothness
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