First order optimization methods such as gradient based method, is widely used in machine learning thanks to its simplicity for implementation and fast convergence. However, the objective function in machine learning can be nonconvex, and the first order method has only the theoretical guarantee that...
Non-convex Optimization for Machine Learning takes an in... (展开全部) 目录· ··· 丛书信息· ··· Foundations and Trends® in Machine Learning(共65册), 这套丛书还有 《Bayesian Reinforcement Learning》《Graph Neural Networks for Natural Language Processing》《Machine Learning for Automated Th...
Non-convexoptimizationisubiquitousinmodernmachinelearning:recentbreak- throughsindeeplearningrequireoptimizingnon-convextrainingobjectivefunctions; problemsthatadmitaccurateconvexrelaxationcanoftenbesolvedmoreefficiently withnon-convexformulations.However,thetheoreticalunderstandingofnon-convex ...
In order to capture the learning and prediction problems accurately, structural constraints such as sparsity or low rank are frequently imposed or else the objective itself is designed to be a non-convex function. This is especially true of algorithms that operate in high-dimensional spaces or ...
is a special kind of nonconvex function and the non-convexity only comes from the factorization of \(\mathbf {u}\mathbf {u}^t\) . based on this observation, we exploit the special curvature of \(g(\mathbf {u})\) in this section. the existing works proved the local linear ...
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接下来,我分两个情况来讨论收敛性:1.Convex。2. Strongly convex。 1.1.convex case 定理1.1(Nonsmooth + convex)如果函数 f 是凸的且是Lipschitzness的。对于迭代方法(1.1),步长选择策略为: \alpha_k =\frac{f(x^k) - f^*}{\|g^k\|^2} 如果g^k \neq 0 ,否则 \alpha_k = 1 。那么我们有:...
which do not cover bi-level problems in modern machine learning that usually involve nonconvex upper-level objective functions. On the other hand, recent studies have analyzed the convergence of BiO-AID with nonconvex upper-level function and strongly convex lower-level function, and established the...
In many statistical learning problems, the target functions to be optimized are highly non-convex in various model spaces and thus are difficult to analyze. In this paper, we compute \\emph{Energy Landscape Maps} (ELMs) which characterize and visualize an energy function with a tree structure,...
作者提出了一个基于Moreau envelope的merit function。通过这个技术，他们对一系列非光滑的随机算法给出了...