Year: 2026
Type: preprint
Abstract: We present a \emph{mirror-free} mirror prox (MFMP) algorithm, which extends the classic approach of Nemirovski (2004) to allow for proximal-like updates without the explicit need for a mirror map. We further analyze the convergence of our method under suitable notions of relative smoothness and relative Lipschitzness, for which we introduce a relaxation of the standard Bregman divergence in terms of more general potential operators. Finally, we show how a strongly monotone variant of our method allows us to solve regularized Taylor-expansion subproblems that appear in both second- and third-order smooth min-max optimization.
Source: arXiv (Cornell University)
Authors: Vyas, Abhijeet, Bullins, Brian
Institution: Purdue University West Lafayette
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7140176381
Cites:
Cited by:
Related to: