no code implementations • 8 Oct 2021 • Dmitrii M. Ostrovskii, Babak Barazandeh, Meisam Razaviyayn
For $0 \le k \le 2$ the surrogate function can be efficiently maximized in $y$; our general approximation result then leads to efficient algorithms for finding a near-stationary point in nonconvex-nonconcave min-max problems, for which we also provide convergence guarantees.
1 code implementation • 4 Dec 2020 • Dmitrii M. Ostrovskii, Mohamed Ndaoud, Adel Javanmard, Meisam Razaviyayn
Here we provide matching upper and lower bounds on the sample complexity as given by $\min\{1/\Delta^2,\sqrt{r}/\Delta\}$ up to a constant factor; here $\Delta$ is a measure of separation between $\mathbb{P}_0$ and $\mathbb{P}_1$ and $r$ is the rank of the design covariance matrix.
no code implementations • 18 Feb 2020 • Dmitrii M. Ostrovskii, Andrew Lowy, Meisam Razaviyayn
As a byproduct, the choice $\varepsilon_y = O(\varepsilon_x{}^2)$ allows for the $O(\varepsilon_x{}^{-3})$ complexity of finding an $\varepsilon_x$-stationary point for the standard Moreau envelope of the primal function.
Optimization and Control 90C06, 90C25, 90C26, 91A99
