炼丹魔法书-Convex Optimization for Machine Learning 这本书是由 Michael Nielsen 和 Isaac Schreiber 合著的，于2019年由MIT出版社出版。该书是机器学习领域中关于非凸优化问题的经典著作之一，主要介绍了一些非凸优化算法以及如何求解非凸优化问题。书中主要讲了两种非凸情况：一是目标函数是凸的，约束集合不是凸的...
We develop efficient numerical optimization algorithms for regularized convex formulations that appear in a variety of areas such as machine learning, statistics, and signal processing. Their objective functions consist of a loss term and a regularization term, where the latter controls the complexity ...
However, if you cross the function line, then the function is non-convex. A non-convex function As you can see in the figure above, the red line crosses the function, which means it is non-convex. Note, however, that the function is convex on some intervals, for instance on [-1,+1...
Differentiable Quasiconvex Function Strictly Quasiconvex Function Strongly Quasiconvex Function Pseudoconvex Function Convex Programming Problem Fritz-John Conditions Karush-Kuhn-Tucker Optimality Necessary Conditions Algorithms for Convex Problems Convex Optimization - Quick Guide Convex Optimization - Resources Co...
These methods might be useful in the core of your own implementation of a machine learning algorithm. You may want to implement your own algorithm tuning scheme to optimize the parameters of a model for some cost function. A good example may be the case where you want to optimize the hyper...
In machine learning and applied statistics, a convex function such as the objective function of support vector machines (SVMs) is generally preferred, since it can leverage the high-performance algorithms and rigorous guarantees established in the extensive literature on convex opti...
2020,Machine Learning (Second Edition) Review article Multi-objective optimization for spectrum sharing in cognitive radio networks: A review 4.5Convex optimization A power control problem inCRNsis formulated as anMOO problem, through developing a convexcost function, based onSINRand transmit power of ...
In each round t, DBGD queries the function ft(x) at n+1 points, and repeatedly updates the decision xt with each approximate gradient computed by applying the (n+1)-point gradient estimator (Agarwal et al. , 2010) to each feedback received from the set of rounds Ft={k|k+dk−1=...
定义1(Convex function):一个函数 f 被称为凸函数,如果对任意 x,y ,满足 (0.1)f(y)≥f(x)+⟨∇f(x),y−x⟩ 定义2(Strong convexity):一个函数 f 被称为 μ -强凸函数,如果对任意 x,y ,满足 (0.2)f(y)≥f(x)+⟨∇f(x),y−x⟩+μ2‖y−x‖2 (别小看后面多出...
Nan W., et al. “The Value of Collaboration in Convex Machine Learning with Differential Privacy.” 2020 IEEE Symposium on Security and Privacy. 304-317. 联邦学习场景中,在适应度函数平滑、强凸、利普斯特连续的条件下,估算各客户端使用不同隐私预算时最终全局模型的信息损失量。实践中,针对适应...