TY - UNPB
T1 - Mirror Descent-Ascent for mean-field min-max problems
AU - Lascu, Razvan-Andrei
AU - Majka, Mateusz
AU - Szpruch, Łukasz
PY - 2024/5/28
Y1 - 2024/5/28
N2 - 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 Nikaidò-Isoda error, are of order O(N−1/2) and O(N−2/3) for the simultaneous and sequential schemes, respectively, which is in line with the state-of-the-art results for related finite-dimensional algorithms.
AB - 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 Nikaidò-Isoda error, are of order O(N−1/2) and O(N−2/3) for the simultaneous and sequential schemes, respectively, which is in line with the state-of-the-art results for related finite-dimensional algorithms.
U2 - 10.48550/arXiv.2402.08106
DO - 10.48550/arXiv.2402.08106
M3 - Preprint
T3 - arXiv
BT - Mirror Descent-Ascent for mean-field min-max problems
PB - arXiv
ER -