论文标题
一类非Convex-Nonconcave Min-Max问题的固定时间收敛
Fixed-Time Convergence for a Class of Nonconvex-Nonconcave Min-Max Problems
论文作者
论文摘要
这项研究开发了一个固定时间收敛的鞍点动力学系统，用于在放松标准凸孔腔假设的放松下解决最小值问题。特别是，通过利用优化算法的动力学系统观点，可以获得加速到鞍点的收敛。与其要求目标函数是强烈的 - 巧妙的concave（由于需要加速几个鞍点算法的加速收敛），还可以保证仅满足双面Polyak-olak-olakdourak-olakdourak olakdouaglojasiewicz（PL）的函数。已知许多实践问题，包括可靠的最小二乘估计，可以满足双面PL不平等。与任何其他具有线性甚至超级线性收敛的最新方法相比，所提出的方法可实现任意快速的收敛性，并且在数值案例研究中也得到了证实。
This study develops a fixed-time convergent saddle point dynamical system for solving min-max problems under a relaxation of standard convexity-concavity assumption. In particular, it is shown that by leveraging the dynamical systems viewpoint of an optimization algorithm, accelerated convergence to a saddle point can be obtained. Instead of requiring the objective function to be strongly-convex--strongly-concave (as necessitated for accelerated convergence of several saddle-point algorithms), uniform fixed-time convergence is guaranteed for functions satisfying only the two-sided Polyak-Łojasiewicz (PL) inequality. A large number of practical problems, including the robust least squares estimation, are known to satisfy the two-sided PL inequality. The proposed method achieves arbitrarily fast convergence compared to any other state-of-the-art method with linear or even super-linear convergence, as also corroborated in numerical case studies.
