报告人：徐姿 (上海大学)
报告题目：Parameter-free Optimization Algorithms and Iteration Complexity for Minimax Optimization Problems
摘要：For most existing algorithms for solving minimax problems, achieving the optimal complexity of the algorithm requires assuming precise information about some parameters of the problem, such as the Lipschitz constant, the upper bound of the distance from the initial point to the optimal solution, and so on. Accurately estimating these parameters is often challenging, and conservative estimates can significantly impact algorithm performance. In this talk, we propose a parameter-free alternating gradient projection (PFAGP) algorithm which does not require the parameters $L$ or $\mu$, incorporating backtracking strategies, for solving smooth nonconvex-(strongly) concave minimax problems. We demonstrate that PFAGP can find an $\varepsilon$-stationary point of the objective function in $\mathcal{O}\left(\varepsilon^{-2}\right)$ iterations under a nonconvex-strongly concave setting, and in $\mathcal{O}\left(\varepsilon^{-4}\right)$ iterations under a nonconvex-concave setting. Moreover, we propose a fully parameter-free cubic regularization (FF-CR) algorithm that does not require any parameters of the problem, including the Lipschitz constant and the upper bound of the distance from the initial point to the optimal solution. We also prove that the iteration complexity of the FF-CR algorithm to obtain an $\epsilon$-optimal solution with respect to the gradient norm is upper bounded by $\mathcal{O}(\frac{\rho\| z^0-z^* \| ^2}{\epsilon})^{\frac{2}{3}}$.
