Mirror Descent-Ascent for mean-field min-max problems
<|reference_start|>Mirror Descent-Ascent for mean-field min-max problems: We study two variants of the mirror descent-ascent algorithm for solving min-max problems on the space of measures: simultaneous and sequential. We work under assumptions of convexity-concavity and relative smoothness of the payoff function with respect to a suitable Bregman divergence, defined on the space of measures via flat derivatives. We show that the convergence rates to mixed Nash equilibria, measured in the Nikaid\`o-Isoda error, are of order $\mathcal{O}\left(N^{-1/2}\right)$ and $\mathcal{O}\left(N^{-2/3}\right)$ for the simultaneous and sequential schemes, respectively, which is in line with the state-of-the-art results for related finite-dimensional algorithms.<|reference_end|>
@article{lascu2024mirror,
    title={Mirror Descent-Ascent for mean-field min-max problems},
    author={Razvan-Andrei Lascu, Mateusz B. Majka, {L}ukasz Szpruch},
    journal={arXiv preprint arXiv:2402.08106},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.08106},
    primaryClass={math.OC cs.LG math.PR}
}