论文标题
通过证书和快速速率通过内核总和的快速率优化
Non-Convex Optimization with Certificates and Fast Rates Through Kernel Sums of Squares
论文作者
论文摘要
我们考虑了潜在的非凸优化问题，其中最佳近似速率取决于参数空间的维度以及要优化的函数的平滑度。在本文中，我们提出了一种接近最佳先验计算保证的算法，同时还提供了后验证书。我们的一般公式建立在无限维平方和傅立叶分析的基础上，并且是根据多元周期函数的最小化实例化的。
We consider potentially non-convex optimization problems, for which optimal rates of approximation depend on the dimension of the parameter space and the smoothness of the function to be optimized. In this paper, we propose an algorithm that achieves close to optimal a priori computational guarantees, while also providing a posteriori certificates of optimality. Our general formulation builds on infinite-dimensional sums-of-squares and Fourier analysis, and is instantiated on the minimization of multivariate periodic functions.
