Convex optimization vs gradient descent
What are the advantages of convex optimization?
Machine learning benefits from convex optimisation due to its many advantages, including convergence guarantees, effective methods, and durability.
Convex optimisation is the foundation of gradient descent, a well-liked optimisation technique in machine learning..
- In concave function, Line joining any two point of the curve is always lies below the curve.
In convex function, line joining any two point of the curve always lies above the curve.
There are some curve in which line joining any two point on the curve maybe lies above, maybe bellow, maybe both or maybe none.
Jun 26, 2020However, the function either lacks a closed form solution or becomes very expensive to compute for large datasets. For instance, logistic Convex Sets and Convex Gradient Descent: IdeaWhy are Convex Functions
Why Use Gradient Descent?
In many data analysis problems we want to minimize some functions: for instance the negative log-likelihood. However, the function either lacks a close… Convex Sets and Convex Functions
Much of the practical application and most of the theory for gradient descent involves convex sets and functions. Intuitively, a convex set is one where for any … Gradient Descent: Idea
The goal of gradient descent is to iteratively find the minimizer of : for a convex function . The idea is to at each iteration use a linear approximation to at a fixed , an… A Gradient Descent Example
Let’s try minimizing using gradient descent. First we define functions to calculate both the function and its derivative. Then we will write code to run and plo… Discussion
In this post we discussed the intuition behind gradient descent. We first defined convex sets and convex functions, then described the idea behind gradient descen… How does convex optimization work?
It tries to improve the function value by moving in a direction related to the gradient (i
e , the rst derivative)
For convex optimization it gives the global optimum under fairly general conditions
For nonconvex optimization it arrives at a local optimum
Is gradient descent a good alternative to convex optimization?
But it is slow in practice
Gradient descent is a popular alternative because it is simple and it gives some kind of meaningful result for both convex and nonconvex optimization
It tries to improve the function value by moving in a direction related to the gradient (i
e , the rst derivative)
What is gradient descent?
We first defined convex sets and convex functions, then described the idea behind gradient descent: moving in the direction opposite the direction with the largest rate of increase
We then described why this is useful for convex functions, and finally showed a toy example
In convex functions, all chords lie above the function values. You can apply gradient descent to non-convex problems provided that they are smooth, but the solutions you get may be only local. Use global optimization techniques in that case such simulated annealing, genetic algorithms etc.The optimization problem induced from classical machine learning methods is often a convex and smooth one, for which gradient descent is guaranteed to solve it efficiently. On the other hand, modern machine learning methods, like deep neural networks, often require solving a non-smooth and non-convex problem. Theoretically, non-convex mathematical
