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Wasserstein Saddle-Free Newton: Saddle Escape and Local Spectral Convergence
Razvan-Andrei Lascu, Taiji Suzuki
Extending saddle-free Newton methods to Wasserstein space requires controlling Hessian dependent operators along nonlinear transport trajectories and accounting for a Hessian spect…
Non-convex entropic mean-field optimization via Best Response flow
Razvan-Andrei Lascu, Mateusz B. Majka
We study the problem of minimizing non-convex functionals on the space of probability measures, regularized by the relative entropy (KL divergence) with respect to a fixed referenc…
Linear convergence of proximal descent schemes on the Wasserstein space
Razvan-Andrei Lascu, Mateusz B. Majka, David Šiška +1
We investigate proximal descent methods, inspired by the minimizing movement scheme introduced by Jordan, Kinderlehrer and Otto, for optimizing entropy-regularized functionals on t…
A Fisher-Rao gradient flow for entropic mean-field min-max games
Razvan-Andrei Lascu, Mateusz B. Majka, Łukasz Szpruch
Gradient flows play a substantial role in addressing many machine learning problems. We examine the convergence in continuous-time of a \textit{Fisher-Rao} (Mean-Field Birth-Death)…
Mirror Descent-Ascent for mean-field min-max problems
Razvan-Andrei Lascu, Mateusz B. Majka, Łukasz Szpruch
We study two variants of the mirror descent-ascent (MDA) algorithm for solving min-max problems on the space of measures: simultaneous and alternating. We work under assumptions of…
Entropic mean-field min-max problems via Best Response flow
Razvan-Andrei Lascu, Mateusz B. Majka, Łukasz Szpruch
We investigate the convergence properties of a continuous-time optimization method, the \textit{Mean-Field Best Response} flow, for solving convex-concave min-max games with entrop…